The leading coefficient of certain Kazhdan-Lusztig polynomials of the permutation group Sn

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