My research interests are mostly in algebraic combinatorics. Lately I have been studying
(a) the representation theory of the symmetric group by understanding the characters as symmetric functions
(b) Symmetric function problems like plethysm and the restriction problem (how a Gl_n irreducible decomposes as an S_n irreducible)
(c) representations of partition algebras and a new multiset partition algebra
(d) q,t-combinatorics, symmetric functions and the corresponding representation theory
My Google scholar page. Back to homepage.



Publications

A Macdonald Vertex Operator and Tableaux Statistics for the Two-Column (q,t)-Kostka Coefficients
Electronic Journal of Combinatorics, 5, (1998), pp. 46.
link 
@article{MZ0,
  title   = {A Macdonald Vertex Operator and Tableaux Statistics for the Two-Column (q,t)-Kostka Coefficients},
  author  = {Zabrocki, Mike},
  journal = {Electronic Journal of Combinatorics},
  year    = {1998},
  volume  = {5},
  pages   = {46},
}
Vertex operators for standard bases of the symmetric functions
Journal of Algebraic Combinatorics, 13, (1), (2000), pp. 83--101.
arXiv 
@article{MZ1,
  title   = {Vertex operators for standard bases of the symmetric functions},
  author  = {Zabrocki, Mike},
  journal = {Journal of Algebraic Combinatorics},
  year    = {2000},
  volume  = {13},
  number  = {1},
  pages   = {83--101},
  eprint        = {math.CO/9904084},
  archivePrefix = {arXiv},
}
Positivity for special cases of (q,t)-Kostka coefficients and standard tableaux statistics
Electronic Journal of Combinatorics, 6, (1999), pp. 36.
arXiv 
@article{MZ2,
  title   = {Positivity for special cases of (q,t)-Kostka coefficients and standard tableaux statistics},
  author  = {Zabrocki, Mike},
  journal = {Electronic Journal of Combinatorics},
  year    = {1999},
  volume  = {6},
  pages   = {36},
  eprint        = {math.CO/9901016},
  archivePrefix = {arXiv},
}
Hall-Littlewood vertex operators and generalized Kostka polynomials
(with Mark Shimozono), Advances in Math., 158, (1), (2001), pp. 66--85.
arXiv 
@article{MZ3,
  title   = {Hall-Littlewood vertex operators and generalized Kostka polynomials},
  author  = {Shimozono, Mark and Zabrocki, Mike},
  journal = {Advances in Math.},
  year    = {2001},
  volume  = {158},
  number  = {1},
  pages   = {66--85},
  eprint        = {math.QA/0001168},
  archivePrefix = {arXiv},
}
Ribbon Operators and Hall-Littlewood Symmetric Functions
Advances in Mathematics, 156, (1), (2000), pp. 33--43.
arXiv extended abstract 
@article{MZ4,
  title   = {Ribbon Operators and Hall-Littlewood Symmetric Functions},
  author  = {Zabrocki, Mike},
  journal = {Advances in Mathematics},
  year    = {2000},
  volume  = {156},
  number  = {1},
  pages   = {33--43},
  eprint        = {math.QA/0008163},
  archivePrefix = {arXiv},
}
Polynomiality of the q,t-Kostka Revisited
(with Adriano Garsia), Algebraic combinatorics and computer science, (2001), pp. 473--491.
arXiv 
@article{MZ5,
  title   = {Polynomiality of the q,t-Kostka Revisited},
  author  = {Garsia, Adriano and Zabrocki, Mike},
  journal = {Algebraic combinatorics and computer science},
  year    = {2001},
  pages   = {473--491},
  eprint        = {math.QA/0008199},
  archivePrefix = {arXiv},
}
q-Analogs of symmetric function operators
Disc. Math., 256, (2002), pp. 831--853.
arXiv 
@article{MZ6,
  title   = {q-Analogs of symmetric function operators},
  author  = {Zabrocki, Mike},
  journal = {Disc. Math.},
  year    = {2002},
  volume  = {256},
  pages   = {831--853},
  eprint        = {math.QA/0008188},
  archivePrefix = {arXiv},
}
q and q,t-Analogs of Non-commutative Symmetric Functions
(with Nantel Bergeron), Discrete Mathematics, 298, (1), (2005), pp. 79--103.
arXiv 
@article{MZ7,
  title   = {q and q,t-Analogs of Non-commutative Symmetric Functions},
  author  = {Bergeron, Nantel and Zabrocki, Mike},
  journal = {Discrete Mathematics},
  year    = {2005},
  volume  = {298},
  number  = {1},
  pages   = {79--103},
  eprint        = {math.CO/0106255},
  archivePrefix = {arXiv},
}
A q-Analog of Q-Schur functions
(with Geninia Tudose), Algebraic combinatorics and quantum Groups, (2003), pp. 135--161.
arXiv extended abstract 
@article{MZ8,
  title   = {A q-Analog of Q-Schur functions},
  author  = {Tudose, Geninia and Zabrocki, Mike},
  journal = {Algebraic combinatorics and quantum Groups},
  year    = {2003},
  pages   = {135--161},
  eprint        = {math.CO/0203046},
  archivePrefix = {arXiv},
}
On Equations of Degree 3 * 2^m
(with Corrado De Concini, Claudio Procesi, Enrico Rogora), Boletin del Instituto de Matematica ``Beppo Levi'' Vol II, (2003), pp. 109--122.
link 
@article{MZ9,
  title   = {On Equations of Degree 3 * 2^m},
  author  = {Concini, Corrado De and Procesi, Claudio and Rogora, Enrico and Zabrocki, Mike},
  journal = {Boletin del Instituto de Matematica ``Beppo Levi'' Vol II},
  year    = {2003},
  pages   = {109--122},
}
Deformed universal characters for classical and affine algebras
(with Mark Shimozono), Journal of Algebra, 299, (1), (2006), pp. 33--61.
arXiv extended abstract 
@article{MZ10,
  title   = {Deformed universal characters for classical and affine algebras},
  author  = {Shimozono, Mark and Zabrocki, Mike},
  journal = {Journal of Algebra},
  year    = {2006},
  volume  = {299},
  number  = {1},
  pages   = {33--61},
  eprint        = {math.CO/0404288},
  archivePrefix = {arXiv},
}
On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia
(with Michael H. Albert, Murray Elder, Andrew Rechnitzer, P. Westcott), Advances in Applied Mathematics, 36, (2), (2006), pp. 96--105.
arXiv 
@article{MZ11,
  title   = {On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia},
  author  = {Albert, Michael H. and Elder, Murray and Rechnitzer, Andrew and Westcott, P. and Zabrocki, Mike},
  journal = {Advances in Applied Mathematics},
  year    = {2006},
  volume  = {36},
  number  = {2},
  pages   = {96--105},
  eprint        = {math.CO/0502504},
  archivePrefix = {arXiv},
}
Posets related to the connectivity set of Coxeter groups
(with Nantel Bergeron, Christophe Hohlweg), Journal of Algebra, 303, (2), (2006), pp. 831--846.
arXiv 
@article{MZ12,
  title   = {Posets related to the connectivity set of Coxeter groups},
  author  = {Bergeron, Nantel and Hohlweg, Christophe and Zabrocki, Mike},
  journal = {Journal of Algebra},
  year    = {2006},
  volume  = {303},
  number  = {2},
  pages   = {831--846},
  eprint        = {math.CO/0509271},
  archivePrefix = {arXiv},
}
Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables
(with Nantel Bergeron, Christophe Hohlweg, Mercedes Rosas), Electr. Journal of Combinatorics, 13, (1), (2006), pp. 19.
arXiv 
@article{MZ13,
  title   = {Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables},
  author  = {Bergeron, Nantel and Hohlweg, Christophe and Rosas, Mercedes and Zabrocki, Mike},
  journal = {Electr. Journal of Combinatorics},
  year    = {2006},
  volume  = {13},
  number  = {1},
  pages   = {19},
  eprint        = {math.CO/0506360},
  archivePrefix = {arXiv},
}
Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables
(with Nantel Bergeron, Christophe Reutenauer, Mercedes Rosas), Canadian Math Journal, 60, (2), (2008), pp. 266--296.
arXiv 
@article{MZ14,
  title   = {Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables},
  author  = {Bergeron, Nantel and Reutenauer, Christophe and Rosas, Mercedes and Zabrocki, Mike},
  journal = {Canadian Math Journal},
  year    = {2008},
  volume  = {60},
  number  = {2},
  pages   = {266--296},
  eprint        = {math.CO/0502082},
  archivePrefix = {arXiv},
}
On the S_n-module structure of the noncommutative harmonics
(with Emmanuel Briand, Mercedes Rosas), Journal of Combinatorial Theory Series A, 115, (6), (2008), pp. 1077--1085.
arXiv 
@article{MZ15,
  title   = {On the S_n-module structure of the noncommutative harmonics},
  author  = {Briand, Emmanuel and Rosas, Mercedes and Zabrocki, Mike},
  journal = {Journal of Combinatorial Theory Series A},
  year    = {2008},
  volume  = {115},
  number  = {6},
  pages   = {1077--1085},
  eprint        = {0704.1101},
  archivePrefix = {arXiv},
}
Hilbert Series of Invariants, Constant terms and Kostka-Foulkes Polynomials
(with Adriano Garsia, Nolan Wallach, Guoce Xin), Discrete Mathematics, 309, (16), (2009), pp. 5206--5230.
link 
@article{MZ16,
  title   = {Hilbert Series of Invariants, Constant terms and Kostka-Foulkes Polynomials},
  author  = {Garsia, Adriano and Wallach, Nolan and Xin, Guoce and Zabrocki, Mike},
  journal = {Discrete Mathematics},
  year    = {2009},
  volume  = {309},
  number  = {16},
  pages   = {5206--5230},
}
A non-commutative generalization of k-Schur functions
(with Nantel Bergeron, Francois Descouens), Discrete Mathematics, 309, (16), (2009), pp. 5092--5105.
arXiv 
@article{MZ17,
  title   = {A non-commutative generalization of k-Schur functions},
  author  = {Bergeron, Nantel and Descouens, Francois and Zabrocki, Mike},
  journal = {Discrete Mathematics},
  year    = {2009},
  volume  = {309},
  number  = {16},
  pages   = {5092--5105},
  eprint        = {0804.0944v1},
  archivePrefix = {arXiv},
}
A Filtration of (q,t)-Catalan numbers
(with Nantel Bergeron, Francois Descouens), Advances in Applied Mathematics, 44, (1), (2010), pp. 16--36.
arXiv 
@article{MZ18,
  title   = {A Filtration of (q,t)-Catalan numbers},
  author  = {Bergeron, Nantel and Descouens, Francois and Zabrocki, Mike},
  journal = {Advances in Applied Mathematics},
  year    = {2010},
  volume  = {44},
  number  = {1},
  pages   = {16--36},
  eprint        = {0806.3046},
  archivePrefix = {arXiv},
}
The Hopf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and cofree
(with Nantel Bergeron), Journal of Algebra and Its Applications, 8, (4), (2009), pp. 581--600.
arXiv 
@article{MZ19,
  title   = {The Hopf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and cofree},
  author  = {Bergeron, Nantel and Zabrocki, Mike},
  journal = {Journal of Algebra and Its Applications},
  year    = {2009},
  volume  = {8},
  number  = {4},
  pages   = {581--600},
  eprint        = {math.CO/0509265},
  archivePrefix = {arXiv},
}
Expressions for Catalan Kronecker Products
(with Andrew Brown, Stephanie van Willigenburg), Pacific Journal of Mathematics, 248, (1), (2010), pp. 31--48.
arXiv 
@article{MZ20,
  title   = {Expressions for Catalan Kronecker Products},
  author  = {Brown, Andrew and Willigenburg, Stephanie van and Zabrocki, Mike},
  journal = {Pacific Journal of Mathematics},
  year    = {2010},
  volume  = {248},
  number  = {1},
  pages   = {31--48},
  eprint        = {0809.3469},
  archivePrefix = {arXiv},
}
The Murnaghan-Nakayama Rule for k-Schur Functions
(with Jason Bandlow, Anne Schilling), Journal of Combinatorial Theory Series A, 118, (5), (2011), pp. 1588--1607.
arXiv 
@article{MZ21,
  title   = {The Murnaghan-Nakayama Rule for k-Schur Functions},
  author  = {Bandlow, Jason and Schilling, Anne and Zabrocki, Mike},
  journal = {Journal of Combinatorial Theory Series A},
  year    = {2011},
  volume  = {118},
  number  = {5},
  pages   = {1588--1607},
  eprint        = {1004.4886},
  archivePrefix = {arXiv},
}
Hall-Littlewood Operators in the Theory of Parking Functions and Diagonal Harmonics
(with Adriano Garsia, Guoce Xin), Int Math Res Notices, 6, (2012), pp. 1264--1299.
DOI link 
@article{MZ22,
  title   = {Hall-Littlewood Operators in the Theory of Parking Functions and Diagonal Harmonics},
  author  = {Garsia, Adriano and Xin, Guoce and Zabrocki, Mike},
  journal = {Int Math Res Notices},
  year    = {2012},
  volume  = {6},
  pages   = {1264--1299},
  doi     = {10.1093/imrn/rnr060},
}
A compositional shuffle conjecture specifying touch points of the Dyck path
(with Jim Haglund, Jennifer Morse), Canadian Journal of Mathematics, 64, (4), (2012), pp. 822--844.
DOI arXiv 
@article{MZ23,
  title   = {A compositional shuffle conjecture specifying touch points of the Dyck path},
  author  = {Haglund, Jim and Morse, Jennifer and Zabrocki, Mike},
  journal = {Canadian Journal of Mathematics},
  year    = {2012},
  volume  = {64},
  number  = {4},
  pages   = {822--844},
  doi     = {10.4153/CJM-2011-078-4},
  eprint        = {1008.0828v2},
  archivePrefix = {arXiv},
}
Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras
(with Marcelo Aguiar, Carlos Andre, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Eric Marberg, Jean-Christophe Novelli, Amy Pang, Franco Saliola, Lenny Tevlin, Jean-Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan), Advances in Mathematics, 229, (4), (2012), pp. 2310--2337.
arXiv 
@article{MZ24,
  title   = {Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras},
  author  = {Aguiar, Marcelo and Andre, Carlos and Benedetti, Carolina and Bergeron, Nantel and Chen, Zhi and Diaconis, Persi and Hendrickson, Anders and Hsiao, Samuel and Isaacs, I. Martin and Jedwab, Andrea and Johnson, Kenneth and Karaali, Gizem and Lauve, Aaron and Le, Tung and Lewis, Stephen and Li, Huilan and Magaard, Kay and Marberg, Eric and Novelli, Jean-Christophe and Pang, Amy and Saliola, Franco and Tevlin, Lenny and Thibon, Jean-Yves and Thiem, Nathaniel and Venkateswaran, Vidya and Vinroot, C. Ryan and Yan, Ning and Zabrocki, Mike},
  journal = {Advances in Mathematics},
  year    = {2012},
  volume  = {229},
  number  = {4},
  pages   = {2310--2337},
  eprint        = {1009.4134},
  archivePrefix = {arXiv},
}
Words and polynomial invariants of finite groups in non-commutative variables
(with A. Bergeron-Brlek, Christophe Hohlweg), Annals of Combinatorics, 16, (1), (2012), pp. 1--36.
DOI arXiv 
@article{MZ25,
  title   = {Words and polynomial invariants of finite groups in non-commutative variables},
  author  = {Bergeron-Brlek, A. and Hohlweg, Christophe and Zabrocki, Mike},
  journal = {Annals of Combinatorics},
  year    = {2012},
  volume  = {16},
  number  = {1},
  pages   = {1--36},
  doi     = {10.1007/s00026-011-0119-0},
  eprint        = {0907.0814},
  archivePrefix = {arXiv},
}
Kronecker Coefficients via Symmetric Functions and Constant Term identities
(with Adriano Garsia, Nolan Wallach, Guoce Xin), International Journal of Algebra and Computation, 22, (3), (2012), pp. 44.
DOI link 
@article{MZ26,
  title   = {Kronecker Coefficients via Symmetric Functions and Constant Term identities},
  author  = {Garsia, Adriano and Wallach, Nolan and Xin, Guoce and Zabrocki, Mike},
  journal = {International Journal of Algebra and Computation},
  year    = {2012},
  volume  = {22},
  number  = {3},
  pages   = {44},
  doi     = {10.1142/S0218196712500221},
}
Expansion of k-Schur functions for maximal k-rectangles within the affine nilCoxeter algebra
(with Chris Berg, Nantel Bergeron, Hugh Thomas), Journal of Combinatorics, 3, (3), (2012), pp. 563--589.
arXiv 
@article{MZ27,
  title   = {Expansion of k-Schur functions for maximal k-rectangles within the affine nilCoxeter algebra},
  author  = {Berg, Chris and Bergeron, Nantel and Thomas, Hugh and Zabrocki, Mike},
  journal = {Journal of Combinatorics},
  year    = {2012},
  volume  = {3},
  number  = {3},
  pages   = {563--589},
  eprint        = {1107.3610},
  archivePrefix = {arXiv},
}
A new dinv Arising from the Two Part Case of the Shuffle Conjecture
(with Adrain Duane, Adriano Garsia), Journal of Algebraic Combinatorics, 37, (4), (2013), pp. 683--715.
DOI arXiv 
@article{MZ28,
  title   = {A new dinv Arising from the Two Part Case of the Shuffle Conjecture},
  author  = {Duane, Adrain and Garsia, Adriano and Zabrocki, Mike},
  journal = {Journal of Algebraic Combinatorics},
  year    = {2013},
  volume  = {37},
  number  = {4},
  pages   = {683--715},
  doi     = {10.1007/s10801-012-0382-0},
  eprint        = {1205.6128},
  archivePrefix = {arXiv},
}
Expansions of k-Schur functions in the affine nilCoxeter algebra
(with Chris Berg, Nantel Bergeron, Steve Pon), Electronic Journal of Combinatorics, 19, (2), (2012), pp. 20.
arXiv 
@article{MZ29,
  title   = {Expansions of k-Schur functions in the affine nilCoxeter algebra},
  author  = {Berg, Chris and Bergeron, Nantel and Pon, Steve and Zabrocki, Mike},
  journal = {Electronic Journal of Combinatorics},
  year    = {2012},
  volume  = {19},
  number  = {2},
  pages   = {20},
  eprint        = {1111.3588v2},
  archivePrefix = {arXiv},
}
Proof of the 2-part Compositional Shuffle Conjecture
(with Adriano Garsia, Guoce Xin), Progress in Mathematics (Book 257), (2014), pp. 227--257.
link 
@article{MZ30,
  title   = {Proof of the 2-part Compositional Shuffle Conjecture},
  author  = {Garsia, Adriano and Xin, Guoce and Zabrocki, Mike},
  journal = {Progress in Mathematics (Book 257)},
  year    = {2014},
  pages   = {227--257},
}
A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions
(with Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano), Canadian Journal of Mathematics, 66, (3), (2014), pp. 525--565.
DOI arXiv 
@article{MZ31,
  title   = {A lift of the Schur and Hall-Littlewood bases to non-commutative symmetric functions},
  author  = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike},
  journal = {Canadian Journal of Mathematics},
  year    = {2014},
  volume  = {66},
  number  = {3},
  pages   = {525--565},
  doi     = {10.4153/CJM-2013-013-0},
  eprint        = {1208.5191},
  archivePrefix = {arXiv},
}
The immaculate basis of the non-commutative symmetric functions
(with Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano), DMTCS Proceedings 25th International Conference on Formal Power Series and Algebraic Combinatorics FPSAC 2013, (2013), pp. 12.
arXiv 1208.5191 1304.1224 1305.4700 
@article{MZ32,
  title   = {The immaculate basis of the non-commutative symmetric functions},
  author  = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike},
  journal = {DMTCS Proceedings 25th International Conference on Formal Power Series and Algebraic Combinatorics FPSAC 2013},
  year    = {2013},
  pages   = {12},
  eprint        = {1303.4801},
  archivePrefix = {arXiv},
}
Indecomposable modules for the dual immaculate basis of quasi-symmetric functions
(with Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano), Proceedings of the AMSVolume 143, 143, (2015), pp. 991--1000.
arXiv Proceedings of the AMS 
@article{MZ33,
  title   = {Indecomposable modules for the dual immaculate basis of quasi-symmetric functions},
  author  = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike},
  journal = {Proceedings of the AMSVolume 143},
  year    = {2015},
  volume  = {143},
  pages   = {991--1000},
  eprint        = {1304.1224},
  archivePrefix = {arXiv},
}
A three shuffle case of the compositional parking function conjecture
(with Adriano Garsia, Guoce Xin), Journal of Combinatorial Theory Series A, 123, (1), (2014), pp. 202--238.
DOI arXiv 
@article{MZ34,
  title   = {A three shuffle case of the compositional parking function conjecture},
  author  = {Garsia, Adriano and Xin, Guoce and Zabrocki, Mike},
  journal = {Journal of Combinatorial Theory Series A},
  year    = {2014},
  volume  = {123},
  number  = {1},
  pages   = {202--238},
  doi     = {10.1016/j.jcta.2013.12.008},
  eprint        = {1208.5796},
  archivePrefix = {arXiv},
}
Some new applications of the Stanley-Macdonald Pieri Rules
(with Adriano Garsia, Jim Haglund, Guoce Xin), Proceedings for for Stanley@70, (2017), pp. 1--25.
arXiv The Mathematical Legacy of Richard P. Stanley, AMS 
@article{MZ35,
  title   = {Some new applications of the Stanley-Macdonald Pieri Rules},
  author  = {Garsia, Adriano and Haglund, Jim and Xin, Guoce and Zabrocki, Mike},
  journal = {Proceedings for for Stanley@70},
  year    = {2017},
  pages   = {1--25},
  eprint        = {1407.7916},
  archivePrefix = {arXiv},
}
The Pieri rule for dual immaculate quasi-symmetric functions
(with Nantel Bergeron, Juana Sanchez-Ortega), Annals of Combinatorics, 20, (2), (2016), pp. 283--300.
DOI arXiv 
@article{MZ36,
  title   = {The Pieri rule for dual immaculate quasi-symmetric functions},
  author  = {Bergeron, Nantel and Sanchez-Ortega, Juana and Zabrocki, Mike},
  journal = {Annals of Combinatorics},
  year    = {2016},
  volume  = {20},
  number  = {2},
  pages   = {283--300},
  doi     = {10.1007/s00026-016-0303-3},
  eprint        = {arXiv:1307.4273},
  archivePrefix = {arXiv},
}
Symmetries of the k-bounded partition lattice
(with Chris Berg, Nathan Williams), Annals of Combinatorics, 20, (2), (2016), pp. 251--281.
DOI arXiv 
@article{MZ37,
  title   = {Symmetries of the k-bounded partition lattice},
  author  = {Berg, Chris and Williams, Nathan and Zabrocki, Mike},
  journal = {Annals of Combinatorics},
  year    = {2016},
  volume  = {20},
  number  = {2},
  pages   = {251--281},
  doi     = {10.1007/s00026-016-0307-z},
  eprint        = {1111.2783v3},
  archivePrefix = {arXiv},
}
Multiplicative structures of the immaculate basis of non-commutative symmetric functions
(with Chris Berg, Nantel Bergeron, Franco Saliola, Luis Serrano), Journal of Combinatorial Theory Series A, 152, (2017), pp. 10--44.
DOI arXiv 
@article{MZ38,
  title   = {Multiplicative structures of the immaculate basis of non-commutative symmetric functions},
  author  = {Berg, Chris and Bergeron, Nantel and Saliola, Franco and Serrano, Luis and Zabrocki, Mike},
  journal = {Journal of Combinatorial Theory Series A},
  year    = {2017},
  volume  = {152},
  pages   = {10--44},
  doi     = {10.1016/j.jcta.2017.05.003},
  eprint        = {1305.4700},
  archivePrefix = {arXiv},
}
A proof of the 4-variable Catalan polynomial of the Delta conjecture
Journal of Combinatorics, 10, (2019), pp. 599--632.
DOI arXiv Jeff Remmel 
@article{MZ39,
  title   = {A proof of the 4-variable Catalan polynomial of the Delta conjecture},
  author  = {Zabrocki, Mike},
  journal = {Journal of Combinatorics},
  year    = {2019},
  volume  = {10},
  pages   = {599--632},
  doi     = {10.4310/JOC.2019.v10.n4.a1},
  eprint        = {1609.03497},
  archivePrefix = {arXiv},
}
Products of symmetric group characters
(with Rosa Orellana), Journal of Combinatorial Theory Series A, 165, (2019), pp. 299--324.
DOI arXiv pdf jupyter notebook 
@article{MZ40,
  title   = {Products of symmetric group characters},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Journal of Combinatorial Theory Series A},
  year    = {2019},
  volume  = {165},
  pages   = {299--324},
  doi     = {10.1016/j.jcta.2019.02.019},
  eprint        = {1709.08098},
  archivePrefix = {arXiv},
}
An insertion algorithm on multiset partitions with applications to diagram algebras
(with Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling), Journal of Algebra, 557, (1), (2020), pp. 97--128.
DOI arXiv 
@article{MZ41,
  title   = {An insertion algorithm on multiset partitions with applications to diagram algebras},
  author  = {Colmenarejo, Laura and Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  journal = {Journal of Algebra},
  year    = {2020},
  volume  = {557},
  number  = {1},
  pages   = {97--128},
  doi     = {10.1016/j.jalgebra.2020.04.010},
  eprint        = {1905.02071},
  archivePrefix = {arXiv},
}
A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module
(with Rosa Orellana), Electronic Journal of Combinatorics, 27, (3), (2020), pp. 18.
DOI arXiv 
@article{MZ42,
  title   = {A combinatorial model for the decomposition of multivariate polynomials rings as an $S_n$-module},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Electronic Journal of Combinatorics},
  year    = {2020},
  volume  = {27},
  number  = {3},
  pages   = {18},
  doi     = {10.37236/8935},
  eprint        = {1906.01125},
  archivePrefix = {arXiv},
}
The Hopf structure of symmetric group characters as symmetric functions
(with Rosa Orellana), Algebraic Combinatorics, 4, (3), (2021), pp. 551--574.
DOI arXiv 
@article{MZ43,
  title   = {The Hopf structure of symmetric group characters as symmetric functions},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Algebraic Combinatorics},
  year    = {2021},
  volume  = {4},
  number  = {3},
  pages   = {551--574},
  doi     = {10.5802/alco.170},
  eprint        = {1901.00378},
  archivePrefix = {arXiv},
}
Symmetric group characters as symmetric functions
(with Rosa Orellana), Advances in Mathematics, 390, (2021), pp. 107943.
DOI arXiv 
@article{MZ44,
  title   = {Symmetric group characters as symmetric functions},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Advances in Mathematics},
  year    = {2021},
  volume  = {390},
  pages   = {107943},
  doi     = {10.1016/j.aim.2021.107943},
  eprint        = {1605.06672},
  archivePrefix = {arXiv},
}
Plethysm and the algebra of uniform block permutations
(with Rosa Orellana, Franco Saliola, Anne Schilling), Algebraic Combinatorics, 5, (5), (2022), pp. 1165--1203.
DOI arXiv 
@article{MZ45,
  title   = {Plethysm and the algebra of uniform block permutations},
  author  = {Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  journal = {Algebraic Combinatorics},
  year    = {2022},
  volume  = {5},
  number  = {5},
  pages   = {1165--1203},
  doi     = {10.5802/alco.243},
  eprint        = {2112.13909},
  archivePrefix = {arXiv},
}
Howe duality of the symmetric group and a multiset partition algebra
(with Rosa Orellana), Communications in Algebra, 51, (1), (2023), pp. 393--413.
DOI arXiv 
@article{MZ46,
  title   = {Howe duality of the symmetric group and a multiset partition algebra},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Communications in Algebra},
  year    = {2023},
  volume  = {51},
  number  = {1},
  pages   = {393--413},
  doi     = {10.1080},
  eprint        = {2007.07370},
  archivePrefix = {arXiv},
}
Quasisymmetric harmonics of the exterior algebra
(with Nantel Bergeron, Kelvin Chan, Farhad Soltani), Canadian Mathematical Bulletin, (2023), pp. 1--17.
DOI arXiv 
@article{MZ47,
  title   = {Quasisymmetric harmonics of the exterior algebra},
  author  = {Bergeron, Nantel and Chan, Kelvin and Soltani, Farhad and Zabrocki, Mike},
  journal = {Canadian Mathematical Bulletin},
  year    = {2023},
  pages   = {1--17},
  doi     = {10.4153},
  eprint        = {2206.02065},
  archivePrefix = {arXiv},
}
The Symmetric Group Through a Dual Perspective
(with Rosa Orellana), Notices of the AMS, 70, (2023), pp. 897--904.
DOI cover art link 
@article{MZ48,
  title   = {The Symmetric Group Through a Dual Perspective},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  journal = {Notices of the AMS},
  year    = {2023},
  volume  = {70},
  pages   = {897--904},
  doi     = {10.1090/noti2704},
}
Representations of the quasi-partition algebras
(with Rosa Orellana, Nancy Wallace), Journal of Algebra, 655, (2024), pp. 758--793.
DOI arXiv 
@article{MZ49,
  title   = {Representations of the quasi-partition algebras},
  author  = {Orellana, Rosa and Wallace, Nancy and Zabrocki, Mike},
  journal = {Journal of Algebra},
  year    = {2024},
  volume  = {655},
  pages   = {758--793},
  doi     = {j.jalgebra.2024.01.025},
  eprint        = {2306.17326},
  archivePrefix = {arXiv},
}
The mystery of plethysm coefficients
(with Laura Colmenarejo, Rosa Orellana, Franco Saliola, Anne Schilling), Proceedings of Symposia in Pure Mathematics, 110, (2024), pp. 275--292.
arXiv 
@article{MZ50,
  title   = {The mystery of plethysm coefficients},
  author  = {Colmenarejo, Laura and Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  journal = {Proceedings of Symposia in Pure Mathematics},
  year    = {2024},
  volume  = {110},
  pages   = {275--292},
  eprint        = {2208.07258},
  archivePrefix = {arXiv},
}
From quasi-symmetric to Schur expansions with applications to symmetric chain decompositions and plethysm
(with Rosa Orellana, Franco Saliola, Anne Schilling), Electronic Journal Combinatorics, 31, (4), (2024), pp. 29.
DOI arXiv 
@article{MZ51,
  title   = {From quasi-symmetric to Schur expansions with applications to symmetric chain decompositions and plethysm},
  author  = {Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  journal = {Electronic Journal Combinatorics},
  year    = {2024},
  volume  = {31},
  number  = {4},
  pages   = {29},
  doi     = {10.37236/12950},
  eprint        = {2404.04512},
  archivePrefix = {arXiv},
}
The lattice of submonoids of the uniform block permutations containing the symmetric group
(with Rosa Orellana, Franco Saliola, Anne Schilling), Semigroup Forum, 110, (2025), pp. 405--421.
DOI arXiv 
@article{MZ52,
  title   = {The lattice of submonoids of the uniform block permutations containing the symmetric group},
  author  = {Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  journal = {Semigroup Forum},
  year    = {2025},
  volume  = {110},
  pages   = {405--421},
  doi     = {10.1007/s00233-025-10505-6},
  eprint        = {2405.09710},
  archivePrefix = {arXiv},
}
When are Hopf algebras determined by integer sequences?
(with Nicolas Andrews, Lucas Gagnon, F\'elix G\'elinas, Eric Schlums), Journal of Pure and Applied Algebra, 230, (9), (2026).
DOI arXiv 
@article{MZ53,
  title   = {When are Hopf algebras determined by integer sequences?},
  author  = {Andrews, Nicolas and Gagnon, Lucas and G\'elinas, F\'elix and Schlums, Eric and Zabrocki, Mike},
  journal = {Journal of Pure and Applied Algebra},
  year    = {2026},
  volume  = {230},
  number  = {9},
  doi     = {10.1016/j.jpaa.2026.108326},
  eprint        = {2505.06941},
  archivePrefix = {arXiv},
}
Memorial Tribute: Adriano Garsia (1928-2024)
(with Jennifer Morse), Notices of the American Mathematical Society, 73, (2026).
DOI link 
@article{MZ54,
  title   = {Memorial Tribute: Adriano Garsia (1928-2024)},
  author  = {Morse, Jennifer and Zabrocki, Mike},
  journal = {Notices of the American Mathematical Society},
  year    = {2026},
  volume  = {73},
  doi     = {10.1090/noti3349},
}

Books

k-Schur functions and affine Schubert calculus
(with Thomas Lam, Luc Lapointe, Jennifer Morse, Anne Schilling, Mark Shimozono), Fields Institute Monographs, Vol 33, Springer, 219 p. (2014)
DOI arXiv 
@book{MZ100,
  title={k-Schur functions and affine Schubert calculus},
  author={Lam, Thomas and Lapointe, Luc and Morse, Jennifer and Schilling, Anne and Shimozono, Mark and Zabrocki, Mike},
  volume={33},
  year={2014},
  series={Fields Institute Monographs},
  publisher={Springer},
  doi={10.1007/978-1-4939-0682-6},
  eprint={1301.3569},
  archivePrefix={arXiv},
}
An Introduction to Ordinary Generating Functions
self published
link 
@book{MZ101,
  title={An Introduction to Ordinary Generating Functions},
  author={Mike Zabrocki},
  year={2013},
  url = {\url{https://garsia.math.yorku.ca/~zabrocki/MMM1/}},
}

Other Papers/Projects/Drafts/Submissions

Thesis: On the action of the Hall-Littlewood vertex operator
library permalink link 
@phdthesis{MZ102,
  title={On the action of the Hall-Littlewood vertex operator},
  author={Zabrocki, Michael Alan},
  school={University of California, San Diego},
  year={1998},
  note={ProQuest LLC},
  url={\url{https://search-library.ucsd.edu/permalink/01UCS_SDI/ld412s/alma991014823179706535}},
}
Some remarks on the characters of the general Lie superalgebra
(with Rosa Orellana), (2000), pp. 3.
arXiv 
@article{MZ55,
  title   = {Some remarks on the characters of the general Lie superalgebra},
  author  = {Orellana, Rosa and Zabrocki, Mike},
  year    = {2000},
  pages   = {3},
  eprint        = {math.CO/0008152},
  archivePrefix = {arXiv},
}
A Bijective Proof of an Unusual Symmetric Group Generating Function
(2003), pp. 4.
arXiv 
@article{MZ56,
  title   = {A Bijective Proof of an Unusual Symmetric Group Generating Function},
  author  = {Zabrocki, Mike},
  year    = {2003},
  pages   = {4},
  eprint        = {math.CO/0310301},
  archivePrefix = {arXiv},
}
Some Calculations on the Outer Hookwalk
(1994), pp. 12.
link 
@article{MZ57,
  title   = {Some Calculations on the Outer Hookwalk},
  author  = {Zabrocki, Mike},
  year    = {1994},
  pages   = {12},
}
Analytic aspects of the shuffle product
(with Marni Mishna), Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, (2008), pp. 561--572.
arXiv 
@article{MZ58,
  title   = {Analytic aspects of the shuffle product},
  author  = {Mishna, Marni and Zabrocki, Mike},
  journal = {Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008},
  year    = {2008},
  pages   = {561--572},
  eprint        = {0802.2844},
  archivePrefix = {arXiv},
}
A module for the Delta conjecture
(2019), pp. 3.
arXiv 
@article{MZ59,
  title   = {A module for the Delta conjecture},
  author  = {Zabrocki, Mike},
  year    = {2019},
  pages   = {3},
  eprint        = {1902.08966},
  archivePrefix = {arXiv},
}
A geometric and generating function approach to plethysm
(with \'Alvaro Guti\'etrrez, Rosa Orellana, Franco Saliola, Anne Schilling), (2025), pp. 28.
arXiv 
@article{MZ60,
  title   = {A geometric and generating function approach to plethysm},
  author  = {Guti\'etrrez, \'Alvaro and Orellana, Rosa and Saliola, Franco and Schilling, Anne and Zabrocki, Mike},
  year    = {2025},
  pages   = {28},
  eprint        = {2511.02649},
  archivePrefix = {arXiv},
}

 
 

Talks and posters
PDF of slides for talk "q-Analogs of Hopf Algebra Structures" given in Kyoto Aug '01
PDF of poster presented at FPSAC'01 in Scottsdale, Arizona June '01 "The ribbon rule for homogeneous symmetric functions"  (extended abstract)
PDF of slides for talk "A quantization of non-commutative symmetric functions"  at the CMS Winter meeting '01 and updated for a seminar at UWaterloo June, '02. This is similar to the chalk talk that I presented at several combinatorics seminars (York, UMinnesota, UQaM) Fall '01.
PDF of slides "Ribbons and Column Strict Tableaux" presented at the Univeristy of Miami and York University colloquium Feb '02.
PDF of slides "A q-analog of Schur's Q-functions" presented at the Wilfrid Laurier University April '02. Description of this research.
FPSAC '02. "Hall-Littlewood analogs in the Q-function algebra" (PDF slides) and "q and qt analogs of non-commutative symmetric functions." (PDF slides)
Prof Talk- for Club Infinity at York University. "Gems of algebra: The secret life of the symmetric group" (PDF of slides)
A Java program to play a game of extended "Set."  I learned a lot about the work that has been done on the game of "Set" at the FPSAC '01 conference where I gave a demo of this program, but I have not had the chance to rewrite the material on the web page to reflect that.
A gallery of posets.  Pictures of permutahedron and other geometric shapes arising from posets.
A series of three talks on symmetric functions in non-commuting variables that I gave in Rome, December 2006 for the Incontro Italiano di Combinatoria Algebrica.
A zoo of Hopf algebras
Combinatorics and coinvariants
A representation theoretical approach
Slides from two talks that I gave at the meeting Combinatorial Algebra meets Algebraic Combinatorics.
A (nother version of the) zoo of Hopf algebras
The wilderness of Hopf algebras
Presentation that I gave at Wake Forest University (updated from the one that I gave at the Fields Institute)
k-Schur functions indexed by a maximal rectangle
A generalization of Suter symmetry for k-bounded partitions, poster where the physical copy was lost somewhere in Japan
Find me a basis that... for Sage Days 49. The goal I had for this talk was to present some ideas that Sage projects and what I wanted to use Sage for. I introduced here the concept of a '(super) totally awesome' basis for a Hopf algebra. Question: what are the (super) totally awesome bases of (N/Q)Sym? Is this within our computational power?
Introduction to Sage or How I learned to stop worrying and love py-thon - An introduction to Sage talk - what Sage does well (and not so well) and why you should (or shouldn't) migrate from other computer algebra systems
Slides from talks on the irreducible character basis:
CMS Winter meeting 2015, On symmetric group and partition algebra characters,
Sage Days 78 2016, Open Problems in Combinatorial Representation Theory,
Coloquio Latinoamericano de Algebra 2016, Irreducible characters of the symmetric group as symmetric functions,
AMS Sectional meeting in Minneapolis on Combinatorial representation theory Oct 2016, Pieri rules and combinatorics of symmetric group characters,
Algèbre et combinatoire au LaCIM, September 2018, The representation theory of the symmetric group revisited.
YouTube videos of talks on symmetric group characters:
IMSc Algebraic Combinatorics Seminar, Chennai, online (India), May 2020
IPAC 2023:
Talk 1 (Rosa) - Schur-Weyl duality, (reduced) Kronecker, Partition Algebra - video - slides
Talk 2 (Mike) - representation theory of S_n, restriction problem - video - slides - notes
Talk 3 (Mike) - better definitions of the character basis - video - slides - notes
Talk 4 (Rosa) - change of bases - multiset partitions and tableaux - video - slides
Talk 5 (Mike) - combinatorial interpretations for some reduced Kronecker - video - slides
Talk 6 (Rosa) - more change of bases, products and combinatorial interpretations - video - slides
An extension of RSK to multi-set partitions:
Dartmouth colloquium, From Robinson-Schensted-Knuth correspondence to Schur-Weyl duality,
Coloquio Latinoamericano de Algebra 2017, Combinatorics of characters of symmetric group as symmetric functions
CMS Winter meeting 2017, Symmetric group representations and Howe duality
AMS Nashville Apr 2018, A multiset partition algebra,
Oberwolfach Feb 2020, The multiset partition algebra and Kronecker product
Representation theory of the monoid of uniform block permutations - Talk for OleFest at Brisbane ACSFRT
Plethysm, symmetric chain decompositions and Ehrhart polynomials - ICERM Category Theory, Combinatorics, and Machine Learning