On the joint distributions of succession and Eulerian statistics
arxiv(2024)
摘要
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.
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