Mathematics – Combinatorics
Scientific paper
2004-01-30
Mathematics
Combinatorics
7 pages
Scientific paper
In this paper we show that the leading coefficient $\mu(y,w)$ 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 $\mu(y,w)$ are not greater than 1 whenever $a(y)< a(w)$, where $a:
\mathfrak S_n\to\mathbf N$ is the function defined by Lusztig.
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