Extending the weak order on Coxeter groups
We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with t...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2020-04-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/6409/pdf |
| _version_ | 1797270228715962368 |
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| author | Francois Viard |
| author_facet | Francois Viard |
| author_sort | Francois Viard |
| collection | DOAJ |
| description | We introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with this theory. |
| first_indexed | 2024-04-25T02:00:56Z |
| format | Article |
| id | doaj.art-b32cae733587446d95fb830876149300 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:00:56Z |
| publishDate | 2020-04-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-b32cae733587446d95fb8308761493002024-03-07T14:55:20ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502020-04-01DMTCS Proceedings, 28th...10.46298/dmtcs.64096409Extending the weak order on Coxeter groupsFrancois Viard0Institut Camille JordanWe introduce a new family of complete lattices, arising from a digraph together with a valuation on its vertices and generalizing a previous construction of the author. We then apply this to the study of two long-standing conjectures of Dyer, and we provide a description of the Tamari lattice with this theory.https://dmtcs.episciences.org/6409/pdfcombinatorics[math.math-co]mathematics [math]/combinatorics [math.co] |
| spellingShingle | Francois Viard Extending the weak order on Coxeter groups Discrete Mathematics & Theoretical Computer Science combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| title | Extending the weak order on Coxeter groups |
| title_full | Extending the weak order on Coxeter groups |
| title_fullStr | Extending the weak order on Coxeter groups |
| title_full_unstemmed | Extending the weak order on Coxeter groups |
| title_short | Extending the weak order on Coxeter groups |
| title_sort | extending the weak order on coxeter groups |
| topic | combinatorics [math.math-co]mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/6409/pdf |
| work_keys_str_mv | AT francoisviard extendingtheweakorderoncoxetergroups |