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 Moll and Boros in that the binomial coefficients are $\infty$-logconcave.Comment: 12 pages, final version incorporating referee's comments. Now published by the Electronic Journal of Combinatorics http://www.combinatorics.org/index.htm