Generating Trees and Pattern Avoidance in Alternating Permutations
We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of sta...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Electronic Journal of Combinatorics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89800 |
| _version_ | 1826198908863250432 |
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| author | Lewis, Joel Brewster |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Lewis, Joel Brewster |
| author_sort | Lewis, Joel Brewster |
| collection | MIT |
| description | We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape ⟨n,n,n⟩, and between the set A[subscript 2n+1](2143) of alternating permutations of length 2n+1 avoiding 2143 and the set of shifted standard Young tableaux of shape ⟨n+2,n+1,n⟩. We also give a number of conjectures and open questions on pattern avoidance in alternating permutations and generalizations thereof. |
| first_indexed | 2024-09-23T11:11:51Z |
| format | Article |
| id | mit-1721.1/89800 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:11:51Z |
| publishDate | 2014 |
| publisher | Electronic Journal of Combinatorics |
| record_format | dspace |
| spelling | mit-1721.1/898002022-09-27T17:45:14Z Generating Trees and Pattern Avoidance in Alternating Permutations Lewis, Joel Brewster Massachusetts Institute of Technology. Department of Mathematics Lewis, Joel Brewster We extend earlier work of the same author to enumerate alternating permutations avoiding the permutation pattern 2143. We use a generating tree approach to construct a recursive bijection between the set A[subscript 2n](2143) of alternating permutations of length 2n avoiding 2143 and the set of standard Young tableaux of shape ⟨n,n,n⟩, and between the set A[subscript 2n+1](2143) of alternating permutations of length 2n+1 avoiding 2143 and the set of shifted standard Young tableaux of shape ⟨n+2,n+1,n⟩. We also give a number of conjectures and open questions on pattern avoidance in alternating permutations and generalizations thereof. 2014-09-18T15:57:37Z 2014-09-18T15:57:37Z 2012-01 2011-08 Article http://purl.org/eprint/type/JournalArticle 1077-8926 http://hdl.handle.net/1721.1/89800 Lewis, Joel Brewster. "Generating Trees and Pattern Avoidance in Alternating Permutations." Electronic Journal of Combinatorics, Volume 19, Issue 1 (2012). en_US http://www.combinatorics.org/ojs/index.php/eljc/article/view/v19i1p21 Electronic Journal of Combinatorics Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. application/pdf Electronic Journal of Combinatorics Electronic Journal of Combinatorics |
| spellingShingle | Lewis, Joel Brewster Generating Trees and Pattern Avoidance in Alternating Permutations |
| title | Generating Trees and Pattern Avoidance in Alternating Permutations |
| title_full | Generating Trees and Pattern Avoidance in Alternating Permutations |
| title_fullStr | Generating Trees and Pattern Avoidance in Alternating Permutations |
| title_full_unstemmed | Generating Trees and Pattern Avoidance in Alternating Permutations |
| title_short | Generating Trees and Pattern Avoidance in Alternating Permutations |
| title_sort | generating trees and pattern avoidance in alternating permutations |
| url | http://hdl.handle.net/1721.1/89800 |
| work_keys_str_mv | AT lewisjoelbrewster generatingtreesandpatternavoidanceinalternatingpermutations |