Speaker: Dr. Esther Banaian, University of California, Riverside
Title: “The cyclic sieving phenomenon and frieze patterns”
Abstract: Frieze patterns are arrays of numbers such that each 2 by 2 square forms a matrix of determinant 1. Several important classes of frieze patterns are in correspondence with non-crossing sets of arcs in various surfaces; in particular, Conway and Coxeter famously showed that finite frieze patterns of positive integers are in bijection with triangulations of polygons. With a goal of enumerating frieze patterns up to shift, we study cyclic equivalence classes of dissections of polygons and once-punctured polygons, using the framework of the cyclic sieving phenomenon. We also describe a correspondence between frieze patterns and p-Dyck paths and exhibit a new operation on p-Dyck paths induced by shifting the rows of a frieze pattern. This is based on joint work with Adams which is available at arxiv:2509.17258.

The Discrete Math Seminar (DMS) is intended for Kennesaw State faculty working in the various areas of algebra, number theory, and discrete mathematics to get together to discuss their current work or related questions. Seminars often involve advanced mathematical knowledge. However, the seminars are open to anyone interested in attending.

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