# Monk's formula

${\displaystyle {\mathfrak {S}}_{s_{r}}{\mathfrak {S}}_{w}=\sum _{{i\leq r
where ${\displaystyle \ell (w)}$ is the length of w. The pairs (i, j) appearing in the sum are exactly those such that ir < j, wi < wj, and there is no i < k < j with wi < wk < wj; each wtij is a cover of w in Bruhat order.