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arXiv · 2103.13092

Equidistributions around special kinds of descents and excedances

Bin Han·Jianxi Mao·Jiang Zeng
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Abstract

We consider a sequence of four variable polynomials by refining Stieltjes' continued fraction for Eulerian polynomials. Using combinatorial theory of Jacobi-type continued fractions and bijections we derive various combinatorial interpretations in terms of permutation statistics for these polynomials, which include special kinds of descents and excedances in a recent paper of Baril and Kirgizov. As a by-product, we derive several equidistribution results for permutation statistics, which enables us to confirm and strengthen a recent conjecture of Vajnovszki and also to obtain several compagnion permutation statistics for two bistatistics in a conjecture of Baril and Kirgizov.

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Bin Han, Jianxi Mao, Jiang Zeng. 2021-03-24. Equidistributions around special kinds of descents and excedances. https://arxiv.org/abs/2103.13092

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