English

The distribution of longest run lengths in integer compositions

Combinatorics 2009-06-30 v1

Abstract

We find the generating function for C(n,k,r)C(n,k,r), the number of compositions of nn into kk positive parts all of whose runs (contiguous blocks of constant parts) have lengths less than rr, using recent generalizations of the method of Guibas and Odlyzko for finding the number of words that avoid a given list of subwords.

Keywords

Cite

@article{arxiv.0906.5196,
  title  = {The distribution of longest run lengths in integer compositions},
  author = {Herbert S. Wilf},
  journal= {arXiv preprint arXiv:0906.5196},
  year   = {2009}
}
R2 v1 2026-06-21T13:18:47.617Z