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Events by date

Thursday, February 25, 2021

Thursday, February 25, 2021 — 1:00 PM EST

Title: Chain decompositions for q,t-Catalan numbers

Speaker: Nick Loehr Affiliation: Virginia Tech Zoom: Contact Karen Yeats

Abstract:

The q,t-Catalan numbers Cat_n(q,t) are polynomials in q and t that reduce to the ordinary Catalan numbers when q=t=1. These polynomials have important connections to representation theory, algebraic geometry, and symmetric functions. Work of Garsia, Haglund, and Haiman has given us combinatorial formulas for Cat_n(q,t) as sums of Dyck vectors weighted by area and dinv. This talk narrates our ongoing quest for a bijective proof of the notorious symmetry property Cat_n(q,t)=Cat_n(t,q).

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