Shape and pattern containment of separable permutations
arXiv:1011.5491
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 σ as a pattern, the shape of w contains the shape of σ. As an application, we exhibit lower bounds for the lengths of supersequences of sets containing separable permutations.
8 pages, 2 figures. Changed emphasis and structure towards shapes containment based on referee's suggestions