On the number of commutation classes of the longest element in the symmetric group
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2016
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| _version_ | 1866911773701963776 |
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| author | Denoncourt, Hugh Ernst, Dana C. Story, Dustin |
| author_facet | Denoncourt, Hugh Ernst, Dana C. Story, Dustin |
| contents | Using the standard Coxeter presentation for the symmetric group $S_n$, two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one expression from the other by applying a finite sequence of commutations. The resulting equivalence classes of reduced expressions are called commutation classes. How many commutation classes are there for the longest element in $S_n$? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1602_08328 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | On the number of commutation classes of the longest element in the symmetric group Denoncourt, Hugh Ernst, Dana C. Story, Dustin History and Overview Combinatorics 05E15 (Primary) 05A05, 05A15, 20F55, 05B45, 52C30, 52C40 (Secondary) Using the standard Coxeter presentation for the symmetric group $S_n$, two reduced expressions for the same group element are said to be commutation equivalent if we can obtain one expression from the other by applying a finite sequence of commutations. The resulting equivalence classes of reduced expressions are called commutation classes. How many commutation classes are there for the longest element in $S_n$? |
| title | On the number of commutation classes of the longest element in the symmetric group |
| topic | History and Overview Combinatorics 05E15 (Primary) 05A05, 05A15, 20F55, 05B45, 52C30, 52C40 (Secondary) |
| url | https://arxiv.org/abs/1602.08328 |