Permutations Containing and Avoiding 123and 132Patterns
We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals (n-2)2 n-3, for n≥3. We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that the number of permutations...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
1999-12-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Online Access: | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/104 |
| _version_ | 1811275549003218944 |
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| author | Aaron Robertson |
| author_facet | Aaron Robertson |
| author_sort | Aaron Robertson |
| collection | DOAJ |
| description | We prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals (n-2)2 n-3, for n≥3. We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that the number of permutations which contain exactly one 123-pattern and exactly one 132-pattern is (n-3)(n-4)2 n-5, for n≥5. |
| first_indexed | 2024-04-12T23:40:48Z |
| format | Article |
| id | doaj.art-d4567ebe09204d6a8e20393c8758ac10 |
| institution | Directory Open Access Journal |
| issn | 1462-7264 1365-8050 |
| language | English |
| last_indexed | 2024-04-12T23:40:48Z |
| publishDate | 1999-12-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-d4567ebe09204d6a8e20393c8758ac102022-12-22T03:12:00ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1462-72641365-80501999-12-0134Permutations Containing and Avoiding 123and 132PatternsAaron RobertsonWe prove that the number of permutations which avoid 132-patterns and have exactly one 123-pattern, equals (n-2)2 n-3, for n≥3. We then give a bijection onto the set of permutations which avoid 123-patterns and have exactly one 132-pattern. Finally, we show that the number of permutations which contain exactly one 123-pattern and exactly one 132-pattern is (n-3)(n-4)2 n-5, for n≥5.http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/104 |
| spellingShingle | Aaron Robertson Permutations Containing and Avoiding 123and 132Patterns Discrete Mathematics & Theoretical Computer Science |
| title | Permutations Containing and Avoiding 123and 132Patterns |
| title_full | Permutations Containing and Avoiding 123and 132Patterns |
| title_fullStr | Permutations Containing and Avoiding 123and 132Patterns |
| title_full_unstemmed | Permutations Containing and Avoiding 123and 132Patterns |
| title_short | Permutations Containing and Avoiding 123and 132Patterns |
| title_sort | permutations containing and avoiding 123and 132patterns |
| url | http://www.dmtcs.org/dmtcs-ojs/index.php/dmtcs/article/view/104 |
| work_keys_str_mv | AT aaronrobertson permutationscontainingandavoiding123and132patterns |