Shape and pattern containment of separable permutations
Combinatorics
2011-09-06 v2
Abstract
Every word has a shape determined by its image under the Robinson-Schensted-Knuth correspondence. We show that when a word w contains a separable (i.e., 3142- and 2413-avoiding) permutation \sigma\ as a pattern, the shape of w contains the shape of \sigma. As an application, we exhibit lower bounds for the lengths of supersequences of sets containing separable permutations.
Cite
@article{arxiv.1011.5491,
title = {Shape and pattern containment of separable permutations},
author = {Andrew Crites and Greta Panova and Gregory S. Warrington},
journal= {arXiv preprint arXiv:1011.5491},
year = {2011}
}
Comments
8 pages, 2 figures. Changed emphasis and structure towards shapes containment based on referee's suggestions