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arXiv · 2002.06930

The gamma-positivity of Eulerian polynomials and succession statistics

Shi-Mei Ma·Jun Ma·Jean Yeh·Yeong-Nan Yeh
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Abstract

This paper is concerned with multivariate refinements of the gamma-positivity of Eulerian polynomials by using the succession and fixed point statistics. Properties of the enumerative polynomials for permutations, signed permutations and derangements, including generating functions and gamma-positivity are studied, which generalize and unify earlier results of Athanasiadis, Brenti, Chow, Petersen, Roselle, Stembridge, Shin and Zeng. In particular, we derive a formula expressing the joint distribution of excedance number and negative number statistics over the type B derangements in terms of the derangement polynomials.

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Shi-Mei Ma, Jun Ma, Jean Yeh, Yeong-Nan Yeh. 2020-02-17. The gamma-positivity of Eulerian polynomials and succession statistics. https://arxiv.org/abs/2002.06930

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