The Algebraic Combinatorics Seminar
Scheduled for Fridays at 3:30 PM, Room 210
Rafael S. González D'león and Nantel Bergeron


Schedule FALL 2017

Date Speaker Title (click titles for abstract)
Sept 15 Nantel Bergeron Organization, two problems:
1- symmetric functions in super space
2- The space of planar trees graded by signature.
Sept 22 Nantel Bergeron and Rafael S. González D'león The space of trees graded by signature.
Sept 29 Nantel Bergeron and Rafael S. González D'león The space of trees graded by signature.
Oct 6 Mike Zabrocki Symmetric functions in super space
I organized the big picture related to the goal of this project: there are a number of polynomial and non-commutative polynomial rings for which the invariants and quasi-invariants are well known Hopf algebras (Sym, QSym, NCSym, etc.). I described the minimal information that we need in order to implement Sym and QSym and left the symmetric functions in super space and the quasi-symmetric functions in super-space as the next steps.
Oct 13
At YORK
Jerzy Wejman This will be a coloquium talk at YORK University. This week only
Oct 20 Mike Zabrocki Symmetric functions in super space
Oct 27 Reading week
Nov 3 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees and stirling permutations (open questions in abstract)
Last time we define Hopf algebra on Planar Binary Trees using a process describe by Aguiar and Sotille using "lightening". This is isomorphic to Loday-Ronco Hopf algebra. We can label the binary trees incrisingly and the "lightening" process still work to define a Hopf algebra. This time it is the larger and correspond to permutations. It is the Malvenuto-Reutenauer Hopf algebra. It is nice to express everything in term of trees as it makes the operation more transparent and explain better the relation between those algebras. Now we can generalize as well very easily. Consider non-degenerate planar trees (no internal node of degree 1). The process of lightening still work well and we can define two Hopf algebras on those trees We can also consider increasing labeling of such trees and now many natural questions arises: SEE QUESTIONS transcripted by James
Nov 10 Mike Zabrocki Symmetric functions in super space
Last time we conjectured a formula for the Monomial and Fundamental quasi-symmetric functions in super space. We will need to work to refine and clarify the notation for these formulae and conjecture their product and coproduct in analogy with the monomial and fundamental bases of QSym.

Code for SuperCompositions and QuasiSymmetricFunctionsinSuperSpace (Monomial basis only) in Sage:
load("http://garsia.math.yorku.ca/~zabrocki/supercompositions.py")
load("http://garsia.math.yorku.ca/~zabrocki/superpartitions.py")
load("http://garsia.math.yorku.ca/~zabrocki/qsf_superspace.py")
load("http://garsia.math.yorku.ca/~zabrocki/sf_superspace.py")
Nov 17 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees, stirling permutations and parking functions.
Nov 24 James Huang and Laura Colmenarjo P partition and Schur function in Symmetric functions in super space
Dec 1 Rafael D'leon and Nantel Bergeron Hopf algebra of planar trees, stirling permutations and parking functions.

Notes.


About the seminar. Every year we pick a new topics to explore.

Year Topic
2016-2017 Quantum Schubert; The theta map; Reduce order of symmetric group; Branching rule between GL(n) and symmetric group.
2015-2016 Positroid and Matroid/ Hopf algebras and quotients.
2014-2015 Fiboland, Symmetric and non symmetric functions
2013-2014 Fiboland, a world of Catalan and Fibonacci numbers
2012-2013 NSym and the Immaculate Basis
2011-2012 k-Schur functions and affine permutations
2010-2011 Littlewood Richardson rule k-Schur functions.
2009-2010 Idempotents and weakly ordered semigroups. (q,t) Catalan Numbers.
2008-2009 Littlewood-Richardson Rule, Shifted Tableaux and P-Schur functions
2007-2008 Open problems around k-Schur functions and non-commutative symmetric functions
2006-2007 Open problems
2005-2006 Cluster Algebras and Quivers
Spring 05 Formal languages and analytic classes of functions
Fall 04 (Quasi-) Symmetric functions in noncommutative variables and applications
Winter 03 Crystal Bases and Representation Theory, Super-algebras, etc.
Fall 03 Quasi-Symmetric functions and applications
Fall 02 Crystal Bases and Representation Theory