Title:Coefficient Positivity and Analytic Combinatorics
| Speaker | John Smith |
| Affiliation | University of Waterloo |
| Location | MC 5479 |
Abstract: Given a rational function analytic at the origin, are its power series coefficients positive? We first motivate this question with historical background, examples and connections to decidability questions in combinatorics. We then present a method for proving positivity for a certain class of multivariate rational functions, by constructing explicit error bounds for an asymptotic expansion using analytic combinatorics in several variables. After applying our method to a couple of examples in the literature, including re-proving a (recently proved) conjecture of Gillis, Reznick and Zeilberger from 1983, we discuss the feasibility of completing certain steps in our analysis using methods from computer algebra.
There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm