The Algebraic Combinatorics Seminar

Scheduled for Fridays at 3:00 PM

In reverse-chronological order.

Date Speaker Title (click titles for abstract) 5 Feb. 2016

29 Jan. 2016

22 Jan. 2016

SPECIAL TalkYuly 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\alpha20 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 230Shu 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 230Yannic 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

NO SEMINAR25 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

SERIES of TALKSCarolina Benedetti Matroid, Positroid and Combinatorial Hopf Algebras.

- Unless otherwise indicated, the seminar meets on Fridays at 3:15 pm in Room 210 of the Fields Institute.
- If you are interested in speaking at the seminar, contact Nantel Bergeron.
- You may also be interested in the Applied Algebra Seminar (Monday afternoons at York University).

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