Print Friendly printer friendly
 Events
USC
Tue 26 Sep 2017, 4:00pm
Discrete Math Seminar
ESB 4127
Combinatorial bases of polynomials
ESB 4127
Tue 26 Sep 2017, 4:00pm-5:00pm

Abstract

We establish a poset structure on combinatorial bases of polynomials, defined by positive expansions. These bases include the well-studied Schubert polynomials, Demazure characters and Demazure atoms, as well as the recently-introduced slide and quasi-key bases. The product of a Schur polynomial and an element of a basis in the poset expands positively in that basis; in particular we give the first Littlewood-Richardson rule for the product of a Schur polynomial and a quasi-key polynomial, extending the rule of Haglund, Luoto, Mason and van Willigenburg for quasi-Schur polynomials. We also establish bijections connecting combinatorial models for these polynomials, including semi-skyline fillings and quasi-key tableaux.
hide
The University of Melbourne
Wed 27 Sep 2017, 3:00pm
Discrete Math Seminar / Probability Seminar
ESB 2012
1324 pattern-avoiding permutations
ESB 2012
Wed 27 Sep 2017, 3:00pm-4:00pm

Abstract

The field of pattern-avoiding permutations was introduced by Knuth in the 1960s as a way of characterising certain data structures. 
Since then, it has grown into an important area in its own right. There are a number of classical problems, among which is the number of 1324-avoiding 
permutations. We will give some history, and then give  details of a new algorithm we have developed for the generating function for this problem. 
As a result we can count these up to length 50.

A new method of analysis we have developed, which can in some circumstances be an alternative to Monte Carlo analysis, reveals some interesting features. 
In particular, we conjecture that the generating function is not D-finite, and has asymptotics that include a stretched-exponential term. 
(Joint work with Andrew Conway and Paul Zinn-Justin).

The late, great Mark Kac often said that his seminars assumed zero knowledge but infinite wisdom. 
This seminar only assumes zero knowledge and finite wisdom.
hide
Rényi Institute
Tue 3 Oct 2017, 4:00pm
Discrete Math Seminar
TBD
Tue 3 Oct 2017, 4:00pm-5:00pm

Abstract

 
hide
UBC
Tue 10 Oct 2017, 5:00pm
Discrete Math Seminar
ESB 4127
TBD
ESB 4127
Tue 10 Oct 2017, 5:00pm-6:00pm

Abstract

 
hide
Foster Tom
UBC
Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127
TBD
ESB 4127
Tue 7 Nov 2017, 4:00pm-5:00pm

Abstract

 
hide
[on hold]
Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar
Tue 7 Nov 2017, 4:00pm-5:00pm

Abstract

 
hide
 
Top