The University of Illinois Algebra-Geometry-Combinatorics Seminar
Spring 2024, Time: Thursdays 3-3:50PM, Place: Burrill Hall 124 / Altgeld Hall 345

Cyclic Sieving on Permutations – An Analysis of Maps and Statistics in the FindStat Database, Amanda Welch (Eastern Illinois University) -- March 7th, 2024

In this talk, we discuss our systematic study of permutation statistics and bijective maps on permutations using SageMath to search the FindStat combinatorial statistics database to identify apparent instances of the cyclic sieving phenomenon (CSP). Cyclic sieving occurs on a set of objects, a statistic, and a map of order n when the evaluation of the statistic generating function at the dth power of the primitive nth root of unity equals the number of fixed points under the dth power of the map. The maps we’ll discuss include reverse, complement, and conjugation by the long cycle, as well as a map constructed by Corteel to swap the number of nestings and crossings, the invert Laguerre heap map, and a map of Alexandersson and Kebede designed to preserve right-to-left minima.

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The seminar co-organizers are Ian Cavey, Andrew Hardt, Shiliang Gao, Elizabeth Kelley, and Alexander Yong.