Combinatorics Seminar

Friday, December 08, 2017 at 4:15pm to 5:15pm

Microsoft Research/MSR 1st Floor Conference Ctr/One Memorial Drive, Cambridge, MA

SPEAKER:  Igor Pak  (UCLA and MSRI)

TITLE:  Counting standard Young tableaux


Consider the number of linear extensions of a large poset. Are there general upper and lower bounds? How good are these bounds in the case of Young diagrams? Can the tools of Algebraic Combinatorics be used to improve on these bounds? These are difficult and largely unexplored questions which we address in some natural special cases.

To be precise, we analyze the asymptotics of the number of standard Young tableaux of large skew diagrams lambda/mu, where both lambda and mu scale linearly. We present new bounds and discuss how they compare with the existing general bounds. Our approach is based on a recent Naruse's hook-length formula which I will also explain and is connected to weighted lozenge tilings and a new particle model of independent interest.

The talk is aimed at a general audience and assumes no previous knowledge of the subject. Based in part on joint work with Alejandro Morales, Greta Panova and Martin Tassy.

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