Cyclotomic factors of necklace polynomials Trevor Hyde, University of Chicago Host: John Doyle Contact John Doyle (john.r.doyle@okstate.edu) for the Zoom link.
Abstract: The sequence $M_d(x)$ of necklace polynomials arises naturally in combinatorics, geometry, dynamics, representation theory, and number theory. For example, Gauss showed that $M_d(q)$ is the number of degree $d$ irreducible polynomials over a finite field with $q$ elements. In this talk I will show that necklace polynomials have many unexpected cyclotomic factors, show that the shifted cyclotomic polynomials $\Phi_d(x) - 1$ have qualitatively similar factorizations, and explain how both phenomena are related to hyperplane arrangements in finite abelian groups.
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