Congruence successions in compositions

Toufik Mansour, Mark Shattuck, Mark C. Wilson

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)327-338
Number of pages12
JournalDiscrete Mathematics and Theoretical Computer Science
Issue number1
StatePublished - 2014


  • Asymptotic estimate
  • Combinatorial proof
  • Composition
  • Parity succession

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Discrete Mathematics and Combinatorics


Dive into the research topics of 'Congruence successions in compositions'. Together they form a unique fingerprint.

Cite this