Shortest path poset of Bruhat intervals
Let $[u,v]$ be a Bruhat interval and $B(u,v)$ be its corresponding Bruhat graph. The combinatorial and topological structure of the longest $u-v$ paths of $B(u,v)$ has been extensively studied and is well-known. Nevertheless, not much is known of the remaining paths. Here we describe combinatorial p...
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| Format: | Article |
| Language: | English |
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Discrete Mathematics & Theoretical Computer Science
2011-01-01
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| Series: | Discrete Mathematics & Theoretical Computer Science |
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| Online Access: | https://dmtcs.episciences.org/2902/pdf |
| _version_ | 1797270342599704576 |
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| author | Saúl A. Blanco |
| author_facet | Saúl A. Blanco |
| author_sort | Saúl A. Blanco |
| collection | DOAJ |
| description | Let $[u,v]$ be a Bruhat interval and $B(u,v)$ be its corresponding Bruhat graph. The combinatorial and topological structure of the longest $u-v$ paths of $B(u,v)$ has been extensively studied and is well-known. Nevertheless, not much is known of the remaining paths. Here we describe combinatorial properties of the shortest $u-v$ paths of $B(u,v)$. We also derive the non-negativity of some coefficients of the complete mcd-index of $[u,v]$. |
| first_indexed | 2024-04-25T02:02:45Z |
| format | Article |
| id | doaj.art-3f55f33f55104036ba18c575a2ac6b63 |
| institution | Directory Open Access Journal |
| issn | 1365-8050 |
| language | English |
| last_indexed | 2024-04-25T02:02:45Z |
| publishDate | 2011-01-01 |
| publisher | Discrete Mathematics & Theoretical Computer Science |
| record_format | Article |
| series | Discrete Mathematics & Theoretical Computer Science |
| spelling | doaj.art-3f55f33f55104036ba18c575a2ac6b632024-03-07T14:49:33ZengDiscrete Mathematics & Theoretical Computer ScienceDiscrete Mathematics & Theoretical Computer Science1365-80502011-01-01DMTCS Proceedings vol. AO,...Proceedings10.46298/dmtcs.29022902Shortest path poset of Bruhat intervalsSaúl A. Blanco0https://orcid.org/0000-0003-2315-5331Department of Mathematics [Cornell]Let $[u,v]$ be a Bruhat interval and $B(u,v)$ be its corresponding Bruhat graph. The combinatorial and topological structure of the longest $u-v$ paths of $B(u,v)$ has been extensively studied and is well-known. Nevertheless, not much is known of the remaining paths. Here we describe combinatorial properties of the shortest $u-v$ paths of $B(u,v)$. We also derive the non-negativity of some coefficients of the complete mcd-index of $[u,v]$.https://dmtcs.episciences.org/2902/pdfbruhat intervalshortest-path posetcomplete \textrmcd-index[math.math-co] mathematics [math]/combinatorics [math.co][info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| spellingShingle | Saúl A. Blanco Shortest path poset of Bruhat intervals Discrete Mathematics & Theoretical Computer Science bruhat interval shortest-path poset complete \textrmcd-index [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| title | Shortest path poset of Bruhat intervals |
| title_full | Shortest path poset of Bruhat intervals |
| title_fullStr | Shortest path poset of Bruhat intervals |
| title_full_unstemmed | Shortest path poset of Bruhat intervals |
| title_short | Shortest path poset of Bruhat intervals |
| title_sort | shortest path poset of bruhat intervals |
| topic | bruhat interval shortest-path poset complete \textrmcd-index [math.math-co] mathematics [math]/combinatorics [math.co] [info.info-dm] computer science [cs]/discrete mathematics [cs.dm] |
| url | https://dmtcs.episciences.org/2902/pdf |
| work_keys_str_mv | AT saulablanco shortestpathposetofbruhatintervals |