Shape and pattern containment of separable permutations
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2010
- DOI:
- arXiv:
- arXiv:1011.5491
- Bibcode:
- 2010arXiv1011.5491C
- Keywords:
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- Mathematics - Combinatorics;
- 05A05;
- 05E05
- E-Print:
- 8 pages, 2 figures. Changed emphasis and structure towards shapes containment based on referee's suggestions