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

2004/01/30 by Nanhua Xi, Xi, Nanhua
Mathematics · #05E15 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05E15 #msc:20F55

paper · pdf · doi:10.48550/arxiv.math/0401430

7 pages

arxiv created 2004/01/30 · arxiv updated 2009/12/01

Abstract

In 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→\mathbf N is the function defined by Lusztig.

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