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.
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