## Polynomial Chebyshev Quotients, Combinatorially

- Jan. 20, 2017
- 2:30 p.m.
- LeConte 312

## Abstract

For any graph G we may construct an associated polynomial called the matching polynomial, which is a variant on a generating function for matchings of G. When G is a cycle or path graph with n vertices, the resulting polynomials are essentially the Chebyshev polynomials of the first and second kind. It is known that there exist divisibility relations for these Chebyshev polynomials; we interpret these relationships combinatorially. In particular we show that one side can be interpreted as the d-matching polynomial introduced by Hall, Pruder and Sawin (2015). This is Joint work completed at the Graduate Research Workshop in Combinatorics with Corbin Groothuis, Andrew Herring, Ranjan Rohatgi, and Eric Stucky.