English

Five subsets of permutations enumerated as weak sorting permutations

Combinatorics 2016-02-17 v1

Abstract

We show that the number of members of S_n avoiding any one of five specific triples of 4-letter patterns is given by sequence A111279 in OEIS, which is known to count weak sorting permutations. By numerical evidence, there are no other (non-trivial) triples of 4-letter patterns giving rise to this sequence. We make use of a variety of methods in proving our result, including recurrences, the kernel method, direct counting, and bijections.

Keywords

Cite

@article{arxiv.1602.05182,
  title  = {Five subsets of permutations enumerated as weak sorting permutations},
  author = {David Callan and Toufik Mansour},
  journal= {arXiv preprint arXiv:1602.05182},
  year   = {2016}
}

Comments

12 pages, 3 figures

R2 v1 2026-06-22T12:51:41.419Z