Gallery Posets of Supersolvable Arrangements
We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of reduced words. Using Rambau's Suspension Lem...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2014-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2444/pdf |
| _version_ | 1797270319593947136 |
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| author | Thomas McConville |
| author_facet | Thomas McConville |
| author_sort | Thomas McConville |
| collection | DOAJ |
| description | We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of reduced words. Using Rambau's Suspension Lemma, we show that these posets are homotopy equivalent to spheres. We furthermore conjecture that its intervals are either homotopy equivalent to spheres or are contractible. One may view this as a analogue of a result of Edelman and Walker on the homotopy type of intervals of a poset of chambers of a hyperplane arrangement. |
| first_indexed | 2024-04-25T02:02:23Z |
| format | Article |
| id | doaj.art-f10649df51d5400b86e6be1924d9c8bb |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:23Z |
| publishDate | 2014-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-f10649df51d5400b86e6be1924d9c8bb2024-03-07T14:53:18ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502014-01-01DMTCS Proceedings vol. AT,...Proceedings10.46298/dmtcs.24442444Gallery Posets of Supersolvable ArrangementsThomas McConvilleWe introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of reduced words. Using Rambau's Suspension Lemma, we show that these posets are homotopy equivalent to spheres. We furthermore conjecture that its intervals are either homotopy equivalent to spheres or are contractible. One may view this as a analogue of a result of Edelman and Walker on the homotopy type of intervals of a poset of chambers of a hyperplane arrangement.https://dmtcs.episciences.org/2444/pdfsuspension lemmasupersolvable arrangementhigher bruhatgeneralized baues problem[info.info-dm] computer science [cs]/discrete mathematics [cs.dm][math.math-co] mathematics [math]/combinatorics [math.co] |
| spellingShingle | Thomas McConville Gallery Posets of Supersolvable Arrangements Discrete Mathematics & Theoretical Computer Science suspension lemma supersolvable arrangement higher bruhat generalized baues problem [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| title | Gallery Posets of Supersolvable Arrangements |
| title_full | Gallery Posets of Supersolvable Arrangements |
| title_fullStr | Gallery Posets of Supersolvable Arrangements |
| title_full_unstemmed | Gallery Posets of Supersolvable Arrangements |
| title_short | Gallery Posets of Supersolvable Arrangements |
| title_sort | gallery posets of supersolvable arrangements |
| topic | suspension lemma supersolvable arrangement higher bruhat generalized baues problem [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] [math.math-co] mathematics [math]/combinatorics [math.co] |
| url | https://dmtcs.episciences.org/2444/pdf |
| work_keys_str_mv | AT thomasmcconville galleryposetsofsupersolvablearrangements |