Séminaire Lotharingien de Combinatoire, 80B.86 (2018), 12 pp.

Theo Douvropoulos

Cyclic Sieving for Reduced Reflection Factorizations of the Coxeter Element

Abstract. In a seminal work, Bessis gave a geometric interpretation of the noncrossing lattice NC(W), associated to a well-generated complex reflection group W. We use this framework to prove, in a unified way, various instances of the cyclic sieving phenomenon on the set of reduced reflection factorizations of the Coxeter element. These include in particular the conjectures of N. Williams on the actions Pro and Twist.


Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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