2003/10/14 by Silvia Heubach, Heubach, Silvia, Toufik Mansour +1 · 2 citations
Mathematics · #05A05 #05A15 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Dynamics and Fractals #math.CO #msc:05A05 #msc:05A15
paper · pdf · doi:10.48550/arxiv.math/0310197
22 pages
arxiv created 2003/10/14 · openalex publication_date 2003/10/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A composition of n∈\NN is an ordered collection of one or more positive integers whose sum is n. The number of summands is called the number of parts of the composition. A palindromic composition of n is a composition of n in which the summands are the same in the given or in reverse order. In this paper we study the generating function for the number of compositions (respectively palindromic compositions) of n with m parts in a given set A⊆\NN with respect to the number of rises, levels, and drops. As a consequence, we derive all the previously known results for this kind of problem, as well as many new results.