Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$
Classical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of 132-avoiding permutations and the set of 123-avo...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2019-11-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/5088/pdf |
| _version_ | 1797270036103036928 |
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| author | Dun Qiu Jeffrey Remmel |
| author_facet | Dun Qiu Jeffrey Remmel |
| author_sort | Dun Qiu |
| collection | DOAJ |
| description | Classical pattern avoidance and occurrence are well studied in the symmetric
group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence
relations to the generating functions counting the number of classical pattern
occurrence in the set of 132-avoiding permutations and the set of 123-avoiding
permutations. |
| first_indexed | 2024-04-25T01:57:53Z |
| format | Article |
| id | doaj.art-d0858b07159e49b5972fe8f5224c58ed |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T01:57:53Z |
| publishDate | 2019-11-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-d0858b07159e49b5972fe8f5224c58ed2024-03-07T15:38:27ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502019-11-01Vol. 21 no. 2, Permutation...Permutation Patterns10.23638/DMTCS-21-2-45088Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$Dun QiuJeffrey RemmelClassical pattern avoidance and occurrence are well studied in the symmetric group $\mathcal{S}_{n}$. In this paper, we provide explicit recurrence relations to the generating functions counting the number of classical pattern occurrence in the set of 132-avoiding permutations and the set of 123-avoiding permutations.https://dmtcs.episciences.org/5088/pdfmathematics - combinatorics05a05, 05a10, 05a15, 05a19 |
| spellingShingle | Dun Qiu Jeffrey Remmel Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ Discrete Mathematics & Theoretical Computer Science mathematics - combinatorics 05a05, 05a10, 05a15, 05a19 |
| title | Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ |
| title_full | Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ |
| title_fullStr | Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ |
| title_full_unstemmed | Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ |
| title_short | Classical pattern distributions in $\mathcal{S}_{n}(132)$ and $\mathcal{S}_{n}(123)$ |
| title_sort | classical pattern distributions in mathcal s n 132 and mathcal s n 123 |
| topic | mathematics - combinatorics 05a05, 05a10, 05a15, 05a19 |
| url | https://dmtcs.episciences.org/5088/pdf |
| work_keys_str_mv | AT dunqiu classicalpatterndistributionsinmathcalsn132andmathcalsn123 AT jeffreyremmel classicalpatterndistributionsinmathcalsn132andmathcalsn123 |