We prove the conjecture of A. Postnikov that (A) the number of regions in the inversion hyperplane arrangement associated with a permutation w ∈ Sn is at most the number of elements below w in the Bruhat order, and (B) that equality holds if and only if w avoids the patterns 4231, 35142, 42513 and 351624. Furthermore, assertion (A) is extended to all finite reflection groups. A byproduct of thi...

A graph $G$ is Ramsey for a $H$ if every colouring of the edges in two colours contains monochromatic copy $H$. Two graphs $H_1$ and $H_2$ are equivalent any only it $H_2$. parameter $s$ distinguishing $s(H_1)\neq s(H_2)$ implies that not equivalent. In this paper we show chromatic number parameter. We also extend to multi-colour case use similar idea find another which distinguishing.