From Bruhat intervals to intersection lattices and a conjecture of Postnikov

From Bruhat intervals to intersection lattices and a conjecture of Postnikov

Blog Article

We prove the conjecture of A.Postnikov that ($mathrm{A}$) the number of regions in the inversion hyperplane arrangement associated with a permutation $w in mathfrak{S}_n$ is at here most the number of elements below $w$ in the Bruhat order, and ($mathrm{B}$) that equality holds if and only if $w$ avoids the patterns $4231$, $35142$, $42513$ and $351624$.Furthermore, aptamil allerpro assertion ($mathrm{A}$) is extended to all finite reflection groups.