
Eventual Positivity of Rational Function Coefficients.Stephen Melczer, Postdoc, University of PennsylvaniaTuesday March 6th at 1:30pm in K9509.
Abstract Given a univariate rational function F(x), a classic problem in combinatorics and theoretical computer science is to determine whether the power series coefficients of F are eventually strictly positive. The decidability of positiveness, and of determining when the power series of F has a 0 coefficient, is still open after many decades of study (a state of affair described by Terry Tao as "faintly outrageous" and a "mathematical embarrassment" by Dick Lipton). Likewise, given a multivariate rational function it is of interest to determine when only a finite number of its power series coefficients are non positive. In this talk we examine the problem through the use of asymptotic expansions of rational function coefficients, settling some conjectures of Straub and Zeitlin. 