2013/07/28 by Toufik Mansour, Mansour, Toufik, Mark Shattuck +3
Computer Science · Mathematics · #05A15 #05A16 #05A19 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Bayesian Methods and Mixture Models #Combinatorics #Combinatorics (math.CO) #Composition (language) #Congruence (geometry) #Discrete mathematics #FOS: Mathematics #Function (biology) #Generating function #Geometry #Limiting #Mathematics #Sequence (biology) #math.CO #msc:05A15 #msc:05A16 #msc:05A19
paper · pdf · doi:10.48550/arxiv.1307.7390
published in arXiv (Cornell University) (Cornell University)
arxiv created 2013/07/28 · openalex publication_date 2013/07/28 · arxiv updated 2013/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
A composition is a sequence of positive integers, called parts, having a fixed sum. By an m-congruence succession, we will mean a pair of adjacent parts x and y within a composition such that x≡ y(mod m). Here, we consider the problem of counting the compositions of size n according to the number of m-congruence successions, extending recent results concerning successions on subsets and permutations. A general formula is obtained, which reduces in the limiting case to the known generating function formula for the number of Carlitz compositions. Special attention is paid to the case m=2, where further enumerative results may be obtained by means of combinatorial arguments. Finally, an asymptotic estimate is provided for the number of compositions of size n having no m-congruence successions.