q-Narayana numbers and the flag h-vector of J(2×n)

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• 作者：Br&auml ; ndé ; n ; Petter
• 关键词：Narayana numbers ; Flag h-vector ; Schur function ; Shelling
• 刊名：Discrete Mathematics
• 出版年：2004
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：April 28, 2004
• 卷：281
• 期：1-3
• 页码：67-81
• 文件大小：274 K

摘要

The Narayana numbers are N(n,k)=(1/n). There are several natural statistics on Dyck paths with a distribution given by N(n,k). We show the equidistribution of Narayana statistics by computing the flag h-vector of J(2×n) in different ways. In the process we discover new Narayana statistics and provide co-statistics for the Narayana statistics so that the bi-statistics have a distribution given by Fürlinger and Hofbauer's q-Narayana numbers. We interpret the flag h-vector in terms of semi-standard Young tableaux, which enables us to express the q-Narayana numbers in terms of Schur functions. We also introduce what we call pre-shellings of simplicial complexes.