The Algebraic Combinatorics Seminar
Scheduled for Fridays at 3:00 PM
Carolina Benedetti and Nantel Bergeron


In reverse-chronological order.

Date Speaker Title (click titles for abstract)
5 Feb. 2016
29 Jan. 2016
22 Jan. 2016
Yuly Billig
(Carleton University)
15 Jan. 2016
Shu Xiao Li
27 Nov. 2015
Sirous Homayouni Fomin-Kirillov algebra
Buchberger's algorithm generates a Grobner basis ($GB$) for $I$, the ideal generated by the relations among generators $ x_{ij}=-x_{ji} $ of Fomin-Kirillov algebra $FK(n)$. We show that elements of any degree $d$, of a $GB$ (with a polynomial ordering) generated by Buchberger's algorithm for the ideal $I$, are \textit{z-star} polynomials, i.e., polynomials with all variables of the form $x_{\alpha z}$, for a fix $z$, where $1\leq\alpha
20 Nov. 2015
Nantel Bergeron Quotient involving Combinatorial Hopf Algebra
I will show that as we pass from n to n+1, The basis of the quotient for n is included in the quotient for n+1. In fact I show several potential inclusion that has consequences on the structure of the Hilbert series of the quotient. I will also recall that when we have free Hopf algebra we can determine the infinite Hilbert series. I will do so for quotient of r-QSym/s-QSym. That last part was inspired by talks during A. Lauve's visit.
13 Nov. 2015
Shu Xiao Li discussion on the dimension of quotients involving r-quasisymmetric functions
6 Nov. 2015
Farid Aliniaeifard The dimension of the quotient of polynomials by ideal generated by non-constant generalized quasi-symmetric functions
We consider a certain action of the symmetric group on polynomials called local action. Then we try to find the dimension of the quotient of polynomials by the ideal generated by the orbits of the local action.
30 Oct. 2015
Mike Zabrocki Symmetric group and Gl_n characters
I will review the construction of the Gl_n and S_n characters in the tensor algebra and then present a simple to state open problem: how do we express the S_n characters as a monomial symmetric function expansion in the eigenvalues of the permutation matrix?
23 Oct. 2015
Room 230
Shu Xiao Li Unimodality and Fibonomials
16 Oct. 2015
Nantel Bergeron Hopf monoid of Matroid and Positroid
I describe the Hopf monoid of matroid (with linear order) and the Hopf submonoid of Positroid.
9 Oct. 2015
Room 230
Yannic Vargas The product of monomial basis in the Hopf algebra of Malvenuto-Reutenauer
We will work out some examples to understand two combinatorial interpretations for the coefficients of the product between the monomial basis in the Hopf algebra of Malvenuto-Reutenauer, based on planar posets and permutation patterns.
2 Oct. 2015
25 Sep. 2015 Nantel Bergeron and Carolina Benedetti Hopf algebras on matroids
We will work out some examples of the several Hopf algebras on Matroids.
18 Sep. 2015 Jean-Baptiste Priez Non-commutative Frobenius characteristic of generalized parking functions
11 Sep. 2015 Nantel Bergeron What to do this year
Aug. 2015
Carolina Benedetti Matroid, Positroid and Combinatorial Hopf Algebras.


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

Year Topic
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 2005 Formal languages and analytic classes of functions
Fall 2004 (Quasi-) Symmetric functions in noncommutative variables and applications
Winter 2003 Crystal Bases and Representation Theory, Super-algebras, etc.
Fall 2003 Quasi-Symmetric functions and applications
Fall 2002 Crystal Bases and Representation Theory