## Abstract

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 language | English |
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Pages (from-to) | 327-338 |

Number of pages | 12 |

Journal | Discrete Mathematics and Theoretical Computer Science |

Volume | 16 |

Issue number | 1 |

State | Published - 2014 |

## Keywords

- Asymptotic estimate
- Combinatorial proof
- Composition
- Parity succession

## ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science (all)
- Discrete Mathematics and Combinatorics