Alternating, Pattern-Avoiding Permutations
We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set S[subscript n](132) of 132-avoiding permutations and the set A[subscript 2n+1](132) of alternating, 132-avoiding permutations. For every set...
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| Format: | Article |
| Language: | en_US |
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Electronic Journal of Combinatorics
2014
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| Online Access: | http://hdl.handle.net/1721.1/89806 |
| _version_ | 1826208894148411392 |
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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 study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set S[subscript n](132) of 132-avoiding permutations and the set A[subscript 2n+1](132) of alternating, 132-avoiding permutations. For every set p[subscript 1],…,p[subscript k] of patterns and certain related patterns q[subscript 1],…,q[subscript k], our bijection restricts to a bijection between S[subscript n](132,p[subscript 1],…,p[subscript k]), the set of permutations avoiding 132 and the p[subscript i], and A[subscript 2n+1](132,q[subscript 1],…,q[subscript k]), the set of alternating permutations avoiding 132 and the q[subscript i]. This reduces the enumeration of the latter set to that of the former. |
| first_indexed | 2024-09-23T14:14:18Z |
| format | Article |
| id | mit-1721.1/89806 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T14:14:18Z |
| publishDate | 2014 |
| publisher | Electronic Journal of Combinatorics |
| record_format | dspace |
| spelling | mit-1721.1/898062022-09-28T19:24:01Z Alternating, Pattern-Avoiding Permutations Lewis, Joel Brewster Massachusetts Institute of Technology. Department of Mathematics Lewis, Joel Brewster We study the problem of counting alternating permutations avoiding collections of permutation patterns including 132. We construct a bijection between the set S[subscript n](132) of 132-avoiding permutations and the set A[subscript 2n+1](132) of alternating, 132-avoiding permutations. For every set p[subscript 1],…,p[subscript k] of patterns and certain related patterns q[subscript 1],…,q[subscript k], our bijection restricts to a bijection between S[subscript n](132,p[subscript 1],…,p[subscript k]), the set of permutations avoiding 132 and the p[subscript i], and A[subscript 2n+1](132,q[subscript 1],…,q[subscript k]), the set of alternating permutations avoiding 132 and the q[subscript i]. This reduces the enumeration of the latter set to that of the former. 2014-09-18T16:31:09Z 2014-09-18T16:31:09Z 2009-02 2008-12 Article http://purl.org/eprint/type/JournalArticle 1077-8926 http://hdl.handle.net/1721.1/89806 Lewis, Joel Brewster. "Alternating, Pattern-Avoiding Permutations." Electronic Journal of Combinatorics, Volume 16, Issue 1 (2009). en_US http://www.combinatorics.org/ojs/index.php/eljc/article/view/v16i1n7 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 Alternating, Pattern-Avoiding Permutations |
| title | Alternating, Pattern-Avoiding Permutations |
| title_full | Alternating, Pattern-Avoiding Permutations |
| title_fullStr | Alternating, Pattern-Avoiding Permutations |
| title_full_unstemmed | Alternating, Pattern-Avoiding Permutations |
| title_short | Alternating, Pattern-Avoiding Permutations |
| title_sort | alternating pattern avoiding permutations |
| url | http://hdl.handle.net/1721.1/89806 |
| work_keys_str_mv | AT lewisjoelbrewster alternatingpatternavoidingpermutations |