2024/01/03 by Shi-Mei Ma, Ma, Shi-Mei, Hao Qi +5
Agricultural and Biological Sciences · Computer Science · Mathematics · #05A05 #05A19 #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Botanical Research and Chemistry #Combinatorics (math.CO) #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2401.01760
openalex publication_date 2024/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, and 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 Eulerian-type statistics. In particular, we give a concise derivation of the generating function for a six-variable Eulerian polynomials.