Unbounded Regions of Infinitely Logconcave Sequences

Abstract

We study the properties of a logconcavity operator on a symmetric, unimodal subset of finite sequences. In doing so we are able to prove that there is a large unbounded region in this subset that is $\infty$-logconcave. This problem was motivated by the conjecture of Boros and Moll that the binomial coefficients are $\infty$-logconcave.