Tamari Lattices for Parabolic Quotients of the Symmetric Group
We present a generalization of the Tamari lattice to parabolic quotients of the symmetric group. More precisely, we generalize the notions of 231-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients, and show bijectively that these sets are equinume...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2015-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
| Subjects: | |
| Online Access: | https://dmtcs.episciences.org/2534/pdf |
| _version_ | 1797270189281116160 |
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| author | Henri Mühle Nathan Williams |
| author_facet | Henri Mühle Nathan Williams |
| author_sort | Henri Mühle |
| collection | DOAJ |
| description | We present a generalization of the Tamari lattice to parabolic quotients of the symmetric group. More precisely, we generalize the notions of 231-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients, and show bijectively that these sets are equinumerous. Furthermore, the restriction of weak order on the parabolic quotient to the parabolic 231-avoiding permutations is a lattice quotient. Lastly, we suggest how to extend these constructions to all Coxeter groups. |
| first_indexed | 2024-04-25T02:00:19Z |
| format | Article |
| id | doaj.art-15f318ff4666448db7e953f5b590c974 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:19Z |
| publishDate | 2015-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-15f318ff4666448db7e953f5b590c9742024-03-07T15:01:26ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502015-01-01DMTCS Proceedings, 27th...Proceedings10.46298/dmtcs.25342534Tamari Lattices for Parabolic Quotients of the Symmetric GroupHenri Mühle0https://orcid.org/0000-0003-1888-7247Nathan Williams1https://orcid.org/0000-0003-2084-6428Laboratoire d'informatique Algorithmique : Fondements et ApplicationsLaboratoire de combinatoire et d'informatique mathématique [Montréal]We present a generalization of the Tamari lattice to parabolic quotients of the symmetric group. More precisely, we generalize the notions of 231-avoiding permutations, noncrossing set partitions, and nonnesting set partitions to parabolic quotients, and show bijectively that these sets are equinumerous. Furthermore, the restriction of weak order on the parabolic quotient to the parabolic 231-avoiding permutations is a lattice quotient. Lastly, we suggest how to extend these constructions to all Coxeter groups.https://dmtcs.episciences.org/2534/pdfsymmetric groupparabolic quotientstamari latticenoncrossing partitionsnonnesting partitionsaligned elements231-avoiding permutations[info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Henri Mühle Nathan Williams Tamari Lattices for Parabolic Quotients of the Symmetric Group Discrete Mathematics & Theoretical Computer Science symmetric group parabolic quotients tamari lattice noncrossing partitions nonnesting partitions aligned elements 231-avoiding permutations [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Tamari Lattices for Parabolic Quotients of the Symmetric Group |
| title_full | Tamari Lattices for Parabolic Quotients of the Symmetric Group |
| title_fullStr | Tamari Lattices for Parabolic Quotients of the Symmetric Group |
| title_full_unstemmed | Tamari Lattices for Parabolic Quotients of the Symmetric Group |
| title_short | Tamari Lattices for Parabolic Quotients of the Symmetric Group |
| title_sort | tamari lattices for parabolic quotients of the symmetric group |
| topic | symmetric group parabolic quotients tamari lattice noncrossing partitions nonnesting partitions aligned elements 231-avoiding permutations [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2534/pdf |
| work_keys_str_mv | AT henrimuhle tamarilatticesforparabolicquotientsofthesymmetricgroup AT nathanwilliams tamarilatticesforparabolicquotientsofthesymmetricgroup |