Skip to Main content Skip to Navigation
Journal articles

Congruence successions in compositions

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(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.
Document type :
Journal articles
Complete list of metadata

Cited literature [22 references]  Display  Hide  Download

https://hal.inria.fr/hal-01179220
Contributor : Hélène Lowinger <>
Submitted on : Wednesday, November 4, 2015 - 2:36:19 PM
Last modification on : Thursday, September 7, 2017 - 1:03:40 AM
Long-term archiving on: : Friday, February 5, 2016 - 11:29:11 AM

File

2486-8808-1-PB_V2.pdf
Publisher files allowed on an open archive

Identifiers

  • HAL Id : hal-01179220, version 1

Collections

Citation

Toufik Mansour, Mark Shattuck, Mark Wilson. Congruence successions in compositions. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no. 1 (in progress) (1), pp.327--338. ⟨hal-01179220⟩

Share

Metrics

Record views

178

Files downloads

757