Shortest path poset of Bruhat intervals

Abstract

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 $[u,v]$.

Keywords

• 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]