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arXiv · 1407.1968

Strong q-log-convexity of the Eulerian polynomials of Coxeter groups

Lily Li Liu·Bao-Xuan Zhu
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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 arraya and a criterion for determining the strong $q$-log-convexity of polynomials sequences, whose generating functions can be given by the continued fraction. As consequences, we get the strong $q$-log-convexity the Eulerian polynomials of type $A_n,B_n$, their $q$-analogous and the generalized Eulerian polynomials associated to the arithmetic progression $\{a,a+d,a+2d,a+3d,\ldots\}$ in a unified manner.

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Lily Li Liu, Bao-Xuan Zhu. 2014-07-08. Strong q-log-convexity of the Eulerian polynomials of Coxeter groups. https://arxiv.org/abs/1407.1968

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