Shortest path poset of Bruhat intervals
International audience 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 d...
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| Other Authors: | , , , , , |
| Format: | Conference Object |
| Language: | English |
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HAL CCSD
2011
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| Subjects: | |
| Online Access: | https://hal.inria.fr/hal-01215085 https://hal.inria.fr/hal-01215085/document https://hal.inria.fr/hal-01215085/file/dmAO0118.pdf |
| Summary: | International audience 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 $[u,v]$. Soit $[u,v]$ un intervalle de Bruhat et $B(u,v)$ le graphe de Bruhat associé. La structure combinatoire et topologique des plus longs chemins de $u$ à $v$ dans $B(u,v)$ est bien comprise, mais on sait peu de chose des autres chemins. Nous décrivons ici les propriétés combinatoires des plus courts de chemins de $u$ à $v$. Nous prouvons aussi que certains coefficients du mcd-indice complet de $[u,v]$ sont positifs. |
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