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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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