2006/12/31 by Sergey Kitaev, Kitaev, Sergey, Toufik Mansour +3
Computer Science · Mathematics · #05A15 #Advanced Combinatorial Mathematics #Algorithms and Data Compression #Combinatorics (math.CO) #FOS: Mathematics #Random Matrices and Applications #math.CO #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0701032
20 pages, sections 3 and 4 are added
openalex publication_date 2006/12/31 · arxiv created 2007/05/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently, Kitaev and Remmel [Classifying descents according to parity, Annals of Combinatorics, to appear 2007] refined the well-known permutation statistic ``descent'' by fixing parity of one of the descent's numbers. Results in that paper were extended and generalized in several ways. In this paper, we shall fix a set partition of the natural numbers N, (N1, ..., Nt), and we study the distribution of descents, levels, and rises according to whether the first letter of the descent, rise, or level lies in Ni over the set of words over the alphabet [k]. In particular, we refine and generalize some of the results in [Counting occurrences of some subword patterns, Discrete Mathematics and Theoretical Computer Science 6 (2003), 001-012.].