Strong [formula omitted]-log-convexity of the Eulerian polynomials of Coxeter groups

Abstract

In this paper we prove the strong q-log-convexity of the Eulerian polynomials of Coxeter groups using their exponential generating functions. Our proof is based on the theory of exponential Riordan arrays and a criterion for determining the strong q-log-convexity of polynomial sequences, whose generating functions can be given by a continued fraction. As applications, we get the strong q-log-convexity of the Eulerian polynomials of types An,Bn, their q-analogue and the generalized Eulerian polynomials associated to the arithmetic progression {a,a+d,a+2d,a+3d,…} in a unified manner.