Shi-Mei Ma, Hao Qi, Jean Yeh, Yeong-Nan Yeh
Published 2024-01-03Version 1
The motivation of this paper is to investigate the joint distribution of succession and Eulerian statistics. We first investigate the enumerators for the joint distribution of descents, big ascents and successions over all permutations in the symmetric group. As an generalization a result of Diaconis-Evans-Graham (Adv. in Appl. Math., 61 (2014), 102--124), we show that two triple set-valued statistics of permutations are equidistributed on symmetric groups. We then introduce the definition of proper left-to-right minimum. We discover that the joint distribution of the succession and proper left-to-right minimum statistics over permutations is a symmetric distribution. In the final part, we discuss the relationship between the fix and cyc (p,q)-Eulerian polynomials and the joint distribution of succession and several Eulerian-type statistics.
Comments: 20 pages. arXiv admin note: text overlap with arXiv:2002.06930
An expansion formula for the inversions and excedances in the symmetric group
On the joint distribution of cyclic valleys and excedances over conjugacy classes of $\mathfrak{S}_{n}$
A Grammar of Dumont and a Theorem of Diaconis-Evans-Graham
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