Toufik Mansour ; Mark Shattuck ; Mark Wilson - Congruence successions in compositions

dmtcs:1252 - Discrete Mathematics & Theoretical Computer Science, May 22, 2014, Vol. 16 no. 1 -
Congruence successions in compositionsArticle

Authors: Toufik Mansour ORCID1; Mark Shattuck 2; Mark Wilson 3

  • 1 Department of Mathematics [Haïfa]
  • 2 Department of Mathematics [Tennessee]
  • 3 Department of Computer Science [Auckland]

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(modm). 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.

Volume: Vol. 16 no. 1
Section: Combinatorics
Published on: May 22, 2014
Accepted on: July 23, 2015
Submitted on: July 13, 2013
Keywords: discrete mathematics, combinatorics,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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