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

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 A n , B n , their q -analogue and the generalized Eulerian polynomials associated to the arithmetic progression { a , a + d , a + 2 d , a + 3 d , ? } in a unified manner.

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