USC

Tue 26 Sep 2017, 4:00pm
Discrete Math Seminar
ESB 4127

Combinatorial bases of polynomials

ESB 4127
Tue 26 Sep 2017, 4:00pm5:00pm
Abstract
We establish a poset structure on combinatorial bases of polynomials, defined by positive expansions. These bases include the wellstudied Schubert polynomials, Demazure characters and Demazure atoms, as well as the recentlyintroduced slide and quasikey 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 LittlewoodRichardson rule for the product of a Schur polynomial and a quasikey polynomial, extending the rule of Haglund, Luoto, Mason and van Willigenburg for quasiSchur polynomials. We also establish bijections connecting combinatorial models for these polynomials, including semiskyline fillings and quasikey tableaux.
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The University of Melbourne

Wed 27 Sep 2017, 3:00pm
Discrete Math Seminar / Probability Seminar
ESB 2012

1324 patternavoiding permutations

ESB 2012
Wed 27 Sep 2017, 3:00pm4:00pm
Abstract
The field of patternavoiding 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 1324avoiding
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 Dfinite, and has asymptotics that include a stretchedexponential term.
(Joint work with Andrew Conway and Paul ZinnJustin).
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.
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Rényi Institute

Tue 3 Oct 2017, 4:00pm
Discrete Math Seminar

TBD

Tue 3 Oct 2017, 4:00pm5:00pm
Abstract
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UBC

Tue 10 Oct 2017, 5:00pm
Discrete Math Seminar
ESB 4127

TBD

ESB 4127
Tue 10 Oct 2017, 5:00pm6:00pm
Abstract
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UBC

Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar
ESB 4127

TBD

ESB 4127
Tue 7 Nov 2017, 4:00pm5:00pm
Abstract
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Tue 7 Nov 2017, 4:00pm
Discrete Math Seminar


Tue 7 Nov 2017, 4:00pm5:00pm
Abstract
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