Luis Serrano

The Cyclic Sieving Phenomenon

Consider a set X, a cyclic action c on X, and a polynomial X(q). The cyclic sieving phenomenon (CSP) occurs when the information about the orbit sizes of X under the action c is encoded in the polynomial X. More precisely, when the number of elements in X of a given order is equal to the evaluation of X(q) in a certain root of unity.

In this talk we will see some examples of CSP, including sets, tableaux, words in certain Coxeter groups, alternating sign matrices, etc. We will also study some of the motivation behind the phenomenon, which ties combinatorics and representation theory.