Trevor Hyde: Cyclotomic factors of necklace polynomials.

Abstract

Necklace polynomials enumerate aperiodic necklaces of colored beads. They have a long history passing through number theory, geometry, representation theory, and combinatorics. I will discuss some recent work which began with the observation that necklace polynomials vanish at many roots of unity. We will see how this phenomenon connects to results of Metropolis and Rota, and how it extends to two independent generalizations of necklace polynomials.