The Mobius function of partitions with restricted block sizes

被引：10

作者：

Ehrenborg, Richard ^{[1
]}

Readdy, Margaret A. ^{[1
]}

机构：

[1] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2007年 / 39卷 / 03期

基金：

美国国家科学基金会;

关键词：

euler and tangent numbers; descent set statistic; set partition lattice; r-divisible partition lattice; knapsack partitions; permutahedron;

D O I：

10.1016/j.aam.2006.08.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to compute the Mobius function of filters in the partition lattice formed by restricting to partitions by type. The Mobius function is determined in terms of the descent set statistics on permutations and the Mobius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Mobius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：283 / 292

页数：10

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