The leading coefficient of certain Kazhdan–Lusztig polynomials of the permutation group

In this paper we show that the leading coefficient μ(y,w) of certain Kazhdan–Lusztig polynomials Py,w of the permutation group 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)