Speaker:  Richard Ehrenborg, University of Kentucky

Title:  Spanning trees and period polynomials

Date:  September 8, 2025

Abstract:

We determine the number of spanning trees in several graphs which are defined using number theoretic means. Our main example is a generalization of the Paley graph in the case when e = 2. The vertex set is the finite field F_q, where two elements are connected by an edge if their difference belongs to a certain collection of cosets of the eth power subgroup. Using results of Myerson on period polynomials, we obtain explicit formulas when the power e is 3 and 4. This is joint work with David Leep.

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