2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70013In this paper we show that the leading coefficient $μ(y,w)$ of certain Kazhdan-Lusztig polynomials $P_{y,w}$ of the permutation group $\mathfrak S_n$ of 1,2,...,n are not greater than 1. More precisely, we show that the leading coefficients $μ(y,w)$ are not greater than 1 whenever $a(y)< a(w)$, where $a: \mathfrak S_n\to\mathbf N$ is the function defined by Lusztig.7 pagesCombinatorics05E15; 20F55text