Shortest path poset of Bruhat intervalsReport as inadecuate

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1 Department of Mathematics Cornell

Abstract : Let $u,v$ be a Bruhat interval and $Bu,v$ be its corresponding Bruhat graph. The combinatorial and topological structure of the longest $u-v$ paths of $Bu,v$ 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 $Bu,v$. We also derive the non-negativity of some coefficients of the complete mcd-index of $u,v$.

Résumé : Soit $u,v$ un intervalle de Bruhat et $Bu,v$ le graphe de Bruhat associé. La structure combinatoire et topologique des plus longs chemins de $u$ à $v$ dans $Bu,v$ 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.

Keywords : Bruhat interval shortest-path poset complete \textrmcd-index

Author: Saúl A. Blanco -



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