Shape and pattern containment of separable permutations
Andrew Crites, Greta Panova, Gregory S. Warrington

TL;DR
This paper investigates how the shape of words under the Robinson-Schensted-Knuth correspondence reflects the containment of separable permutations, providing bounds for supersequence lengths.
Contribution
It establishes that words containing separable permutations have shapes that include the permutation's shape, advancing understanding of pattern containment in combinatorial structures.
Findings
Shapes of words contain the shapes of contained separable permutations
Lower bounds for supersequence lengths of sets with separable permutations
Characterization of pattern containment via shape inclusion
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.
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Taxonomy
Topicssemigroups and automata theory · Algorithms and Data Compression · Advanced Combinatorial Mathematics
