Mathematics Colloquia and Seminars

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An instance of the cyclic sieving phenomenon occurs in the following situation: A set X with a cyclic group action has an associated polynomial X(q), such that setting q equal to certain roots of unity counts fixed points of the group action. In particular, one always has X(1) = |X| and one thinks of X(q) as a particularly ''good'' q-analogue of |X|. Barcelo, Reiner and Stanton generalized this phenomenon to the case when X has an action of a bicyclic group. In this talk I will give examples of the (bi)cyclic sieving phenomenon related to some of our favorite combinatorial objects: (multi)subsets, (bi)words, finite fields, and graphs.