Sorting and preimages of pattern classes
We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack,...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2012-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/3066/pdf |
| _version_ | 1797270291354746880 |
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| author | Anders Claesson Henning Úlfarsson |
| author_facet | Anders Claesson Henning Úlfarsson |
| author_sort | Anders Claesson |
| collection | DOAJ |
| description | We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack, in terms of patterns. We also solve the long-standing problem of describing West-3-stack-sortable permutations. This requires a new type of generalized permutation pattern we call a decorated pattern. |
| first_indexed | 2024-04-25T02:01:56Z |
| format | Article |
| id | doaj.art-83f2e1e88867429987379a14fd9d2344 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:56Z |
| publishDate | 2012-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-83f2e1e88867429987379a14fd9d23442024-03-07T14:51:45ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502012-01-01DMTCS Proceedings vol. AR,...Proceedings10.46298/dmtcs.30663066Sorting and preimages of pattern classesAnders Claesson0Henning Úlfarsson1Department of Computer and Information Sciences [Univ Strathclyde]School of Computer Science [Reykjavik]We introduce an algorithm to determine when a sorting operation, such as stack-sort or bubble-sort, outputs a given pattern. The algorithm provides a new proof of the description of West-2-stack-sortable permutations, that is permutations that are completely sorted when passed twice through a stack, in terms of patterns. We also solve the long-standing problem of describing West-3-stack-sortable permutations. This requires a new type of generalized permutation pattern we call a decorated pattern.https://dmtcs.episciences.org/3066/pdfpermutation patternssorting algorithms[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Anders Claesson Henning Úlfarsson Sorting and preimages of pattern classes Discrete Mathematics & Theoretical Computer Science permutation patterns sorting algorithms [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Sorting and preimages of pattern classes |
| title_full | Sorting and preimages of pattern classes |
| title_fullStr | Sorting and preimages of pattern classes |
| title_full_unstemmed | Sorting and preimages of pattern classes |
| title_short | Sorting and preimages of pattern classes |
| title_sort | sorting and preimages of pattern classes |
| topic | permutation patterns sorting algorithms [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/3066/pdf |
| work_keys_str_mv | AT andersclaesson sortingandpreimagesofpatternclasses AT henningulfarsson sortingandpreimagesofpatternclasses |