2006/04/20 by Sergey Kitaev, Kitaev, Sergey, Jeffrey B. Remmel +2
Computer Science · Mathematics · #05A15 #05E05 #Advanced Statistical Methods and Models #Bayesian Modeling and Causal Inference #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A15 #msc:05E05
paper · pdf · doi:10.48550/arxiv.math/0604455
42 pages
arxiv created 2006/04/20 · openalex publication_date 2006/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [S. Kitaev and J. Remmel: Classifying descents according to parity] the authors refine the well-known permutation statistic "descent" by fixing parity of (exactly) one of the descent's numbers. In this paper, we generalize the results of [S. Kitaev and J. Remmel: Classifying descents according to parity] by studying descents according to whether the first or the second element in a descent pair is equivalent to k mod k≥ 2. We provide either an explicit or an inclusion-exclusion type formula for the distribution of the new statistics. Based on our results we obtain combinatorial proofs of a number of remarkable identities. We also provide bijective proofs of some of our results and state a number of open problems.