Word posets, with applications to Coxeter groups
We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then apply the partially ordered sets to Coxeter groups. Some result...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2011-08-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1108.3638v1 |
| _version_ | 1818823653917196288 |
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| author | Matthew J. Samuel |
| author_facet | Matthew J. Samuel |
| author_sort | Matthew J. Samuel |
| collection | DOAJ |
| description | We discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then apply the partially ordered sets to Coxeter groups. Some results are a proof that enumerating the reduced words of elements of Coxeter groups is #P-complete, a recursive formula for computing the number of commutation classes of reduced words, as well as stronger bounds on the maximum number of commutation classes than were previously known. This also allows us to improve the known bounds on the number of primitive sorting networks. |
| first_indexed | 2024-12-18T23:43:24Z |
| format | Article |
| id | doaj.art-008e7cf72cf748fab6140b53b448b79f |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-18T23:43:24Z |
| publishDate | 2011-08-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-008e7cf72cf748fab6140b53b448b79f2022-12-21T20:47:18ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802011-08-0163Proc. WORDS 201122623010.4204/EPTCS.63.28Word posets, with applications to Coxeter groupsMatthew J. SamuelWe discuss the theory of certain partially ordered sets that capture the structure of commutation classes of words in monoids. As a first application, it follows readily that counting words in commutation classes is #P-complete. We then apply the partially ordered sets to Coxeter groups. Some results are a proof that enumerating the reduced words of elements of Coxeter groups is #P-complete, a recursive formula for computing the number of commutation classes of reduced words, as well as stronger bounds on the maximum number of commutation classes than were previously known. This also allows us to improve the known bounds on the number of primitive sorting networks.http://arxiv.org/pdf/1108.3638v1 |
| spellingShingle | Matthew J. Samuel Word posets, with applications to Coxeter groups Electronic Proceedings in Theoretical Computer Science |
| title | Word posets, with applications to Coxeter groups |
| title_full | Word posets, with applications to Coxeter groups |
| title_fullStr | Word posets, with applications to Coxeter groups |
| title_full_unstemmed | Word posets, with applications to Coxeter groups |
| title_short | Word posets, with applications to Coxeter groups |
| title_sort | word posets with applications to coxeter groups |
| url | http://arxiv.org/pdf/1108.3638v1 |
| work_keys_str_mv | AT matthewjsamuel wordposetswithapplicationstocoxetergroups |