Möbius function on cross-section lattices.
type: Item
instance of: scholarly article
title: Möbius function on cross-section lattices.
zbMATH Open document ID: 1054.20048
published in: Journal of Combinatorial Theory. Series A
publication date: 2004-08-06T00:00:00Z
review text: The Möbius function \(\mu\) on partially ordered sets is an important enumerative and structural invariant in combinatorics. Two classical examples are particularly relevant to reductive (algebraic) monoids. First the Möbius function on the face lattice of a polytope is given by \(\mu(e,f)=(-1)^{l[e,f]}\), where \(l[e,f]\) denotes the length of the interval \([e,f]\). Second the Möbius function on a direct product of linear chains, given by \(\mu(e,f)=\begin{cases} (-1)^{l[e,f]},&\text{if }[e,f]\) is a Boolean lattice
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 06A07
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 52B20
zbMATH DE Number: 2082024
zbMATH Keywords: cross-section lattices
zbMATH Keywords: face lattices
zbMATH Keywords: Möbius functions
zbMATH Keywords: polytopes
zbMATH Keywords: reductive monoids
zbMATH Keywords: Weyl groups
author: Mohan S. Putcha
reviewed by: Huang Wenxue
MaRDI profile type: Publication
full work available at URL: j.jcta.2004.03.001
OpenAlex ID: W2116374334
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DOI: 10.1016/J.JCTA.2004.03.001
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description: scientific article; zbMATH DE number 2082024