2005/05/05 by Sergey Kitaev, Kitaev, Sergey, Tyrrell B. McAllister +3
Computer Science · Mathematics · #05A05 #05A15 #05A17 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05A05 #msc:05A15 #msc:05A17 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0505094
12 pages, 1 figure
arxiv created 2005/05/05 · openalex publication_date 2005/05/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A composition of a nonnegative integer (n) is a sequence of positive integers whose sum is (n). A composition is palindromic if it is unchanged when its terms are read in reverse order. We provide a generating function for the number of occurrences of arbitrary segmented partially ordered patterns among compositions of (n) with a prescribed number of parts. These patterns generalize the notions of rises, drops, and levels studied in the literature. We also obtain results enumerating parts with given sizes and locations among compositions and palindromic compositions with a given number of parts. Our results are motivated by "encoding by restricted permutations," a relatively undeveloped method that provides a language for describing many combinatorial objects. We conclude with some examples demonstrating bijections between restricted permutations and other objects.