On the maximum value of the first coefficients of Kazhdan-Lusztig polynomials for symmetric groups
Vol. 1 (1994), No. 2, Page 461--469.
Tagawa, Hiroyuki
On the maximum value of the first coefficients of Kazhdan-Lusztig polynomials for symmetric groups
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Abstract:
In this article, we show that max$\{c^-(w);w \in \frak S_n\} = [n^2/4]$, where $c^-(w)$ is the number of elements covered by $w \in \frak S_n$ in the Bruhat order. Using this result, we can see that the maximum value of the first coefficients of Kazhdan-Lusztig polynomials for $\frak S_n$ equals $[n^2/4]- n + 1$.
Mathematics Subject Classification (1991): Primary 06A07; Secondary 20B30
Mathematical Reviews Number: MR1317469
Received: 1993-12-07
