Séminaire Lotharingien de Combinatoire, 85B.70 (2021), 12 pp.

Jaeseong Oh

Orbit Harmonics and Cyclic Sieving: a Survey

Abstract. Orbit harmonics is a tool in combinatorial representation theory which promotes the (ungraded) action of a linear group G on a finite set X to a graded action of G on a polynomial ring quotient. The cyclic sieving phenomenon is a notion in enumerative combinatorics which encapsulates the fixed-point structure of the action of a finite cyclic group C on a finite set X in terms of root-of-unity evaluations of an auxiliary polynomial X(q). In this survey, we present a variety of sieving results obtained by applying orbit harmonics.

Received: December 1, 2020. Accepted: March 1, 2021. Final version: April 29, 2021.

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