The Möbius function of partitions with restricted block sizes

Richard Ehrenborg; Margaret A. Readdy

doi:10.1016/j.aam.2006.08.006

The Möbius function of partitions with restricted block sizes

Richard Ehrenborg, Margaret A. Readdy

Mathematics

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

The purpose of this paper is to compute the Möbius function of filters in the partition lattice formed by restricting to partitions by type. The Möbius function is determined in terms of the descent set statistics on permutations and the Möbius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Möbius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.

Original language	English
Pages (from-to)	283-292
Number of pages	10
Journal	Advances in Applied Mathematics
Volume	39
Issue number	3
DOIs	https://doi.org/10.1016/j.aam.2006.08.006
State	Published - Sep 2007

Bibliographical note

Funding Information:
* Corresponding author. E-mail address: [email protected] (R. Ehrenborg). 1 Partially supported by National Science Foundation grant 0200624.

Funding

* Corresponding author. E-mail address: [email protected] (R. Ehrenborg). 1 Partially supported by National Science Foundation grant 0200624.

Funders	Funder number
National Science Foundation (NSF)
Directorate for Mathematical and Physical Sciences	0200624

Keywords

Descent set statistic
Euler and tangent numbers
Knapsack partitions
Permutahedron
Set partition lattice
r-Divisible partition lattice

ASJC Scopus subject areas

Applied Mathematics

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10.1016/j.aam.2006.08.006

Cite this

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title = "The M{\"o}bius function of partitions with restricted block sizes",

abstract = "The purpose of this paper is to compute the M{\"o}bius function of filters in the partition lattice formed by restricting to partitions by type. The M{\"o}bius function is determined in terms of the descent set statistics on permutations and the M{\"o}bius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the M{\"o}bius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.",

keywords = "Descent set statistic, Euler and tangent numbers, Knapsack partitions, Permutahedron, Set partition lattice, r-Divisible partition lattice",

author = "Richard Ehrenborg and Readdy, {Margaret A.}",

note = "Funding Information: * Corresponding author. E-mail address: [email protected] (R. Ehrenborg). 1 Partially supported by National Science Foundation grant 0200624.",

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AU - Ehrenborg, Richard

AU - Readdy, Margaret A.

N1 - Funding Information: * Corresponding author. E-mail address: [email protected] (R. Ehrenborg). 1 Partially supported by National Science Foundation grant 0200624.

PY - 2007/9

Y1 - 2007/9

N2 - The purpose of this paper is to compute the Möbius function of filters in the partition lattice formed by restricting to partitions by type. The Möbius function is determined in terms of the descent set statistics on permutations and the Möbius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Möbius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.

AB - The purpose of this paper is to compute the Möbius function of filters in the partition lattice formed by restricting to partitions by type. The Möbius function is determined in terms of the descent set statistics on permutations and the Möbius function of filters in the lattice of integer compositions. When the underlying integer partition is a knapsack partition, the Möbius function on integer compositions is determined by a topological argument. In this proof the permutahedron makes a cameo appearance.

KW - Descent set statistic

KW - Euler and tangent numbers

KW - Knapsack partitions

KW - Permutahedron

KW - Set partition lattice

KW - r-Divisible partition lattice

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DO - 10.1016/j.aam.2006.08.006

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VL - 39

SP - 283

EP - 292

JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 3

ER -

The Möbius function of partitions with restricted block sizes

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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