Algebraic properties for some permutation statistics
In this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2013-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2345/pdf |
| _version_ | 1797270267489157120 |
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| author | Vincent Vong |
| author_facet | Vincent Vong |
| author_sort | Vincent Vong |
| collection | DOAJ |
| description | In this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then we study the algebraic properties of these quotient sets. After having shown that some of them give rise to quotient algebras of $\mathbf{FQSym}$, we prove that they are also free. |
| first_indexed | 2024-04-25T02:01:33Z |
| format | Article |
| id | doaj.art-3677940d6445422d8351c311aa9e307a |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:01:33Z |
| publishDate | 2013-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-3677940d6445422d8351c311aa9e307a2024-03-07T14:52:36ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502013-01-01DMTCS Proceedings vol. AS,...Proceedings10.46298/dmtcs.23452345Algebraic properties for some permutation statisticsVincent Vong0Laboratoire d'Informatique Gaspard-MongeIn this article, we study some quotient sets on permutations built from peaks, valleys, double rises and double descents. One part is dedicated to the enumeration of the cosets using the bijection of Francon-Viennot which is a bijection between permutations and the so-called Laguerre histories. Then we study the algebraic properties of these quotient sets. After having shown that some of them give rise to quotient algebras of $\mathbf{FQSym}$, we prove that they are also free.https://dmtcs.episciences.org/2345/pdflaguerre historiesincreasing binary treesfree quasi-symmetric functionsquotient algebra[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Vincent Vong Algebraic properties for some permutation statistics Discrete Mathematics & Theoretical Computer Science laguerre histories increasing binary trees free quasi-symmetric functions quotient algebra [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Algebraic properties for some permutation statistics |
| title_full | Algebraic properties for some permutation statistics |
| title_fullStr | Algebraic properties for some permutation statistics |
| title_full_unstemmed | Algebraic properties for some permutation statistics |
| title_short | Algebraic properties for some permutation statistics |
| title_sort | algebraic properties for some permutation statistics |
| topic | laguerre histories increasing binary trees free quasi-symmetric functions quotient algebra [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2345/pdf |
| work_keys_str_mv | AT vincentvong algebraicpropertiesforsomepermutationstatistics |