Samu Potka: The Cyclic Sieving Phenomenon on Circular Dyck Paths

Time: Fri 2019-11-22 16.35 - 16.55

Lecturer: Samu Potka, KTH

Location: KTH, D3

Abstract

The cyclic sieving phenomenon (CSP) was defined by Reiner, Stanton, and White in 2004. The ingredients are a finite set \(X\), a cyclic group \(C\) acting on \(X\), and a polynomial \(f(q)\) with nonnegative integer coefficients and satisfying \(f(1) = |X|\). The triple \((X, C, f(q))\) is said to exhibit the CSP if \(f(q)\) evaluated at certain roots of unity gives the number of elements of \(X\) fixed by powers of a generator of \(C\). We will discuss an example instance on circular Dyck paths, which were recently studied by Alexandersson and Panova. We \(q\)-enumerated them and proved that they exhibit the CSP under shifting their area sequences. This is joint work with Per Alexandersson and Svante Linusson.

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