Unimodality polynomials and generalized Pascal triangles

Abstract

In this paper, we show that if P(x) = Pm k=0 akx k is a polynomial with nondecreasing, nonnegative coefficients, then the coefficients sequence of P(x

s + · · · + x + 1) is unimodal for each integer s > 1. This paper is an extension of Boros and Moll’s result “A criterion for unimodality”, who proved that the polynomial P(x + 1) is unimodal.