Remarks on the Möbius function of a subposet
type: Item
instance of: scholarly article
title: Remarks on the Möbius function of a subposet
zbMATH Open document ID: 0664.06001
DOI: 10.1016/0012-365X(89)90275-6
author: Neil J. Ross
published in: Discrete Mathematics
publication date: 1989-01-01T00:00:00Z
review text: In this brief note the author shows via an interesting observation leading to a simple computation that \[ \mu_ P(x,y)=\mu_ R(x,y)+\sum_{A}\mu_ R(x,s)\mu_ P(t,u)\mu_ R(v,y) \] where P is a poset, D is a subposet and \(R=P-D\) with induced ordering, \(\mu_ X\) is the Möbius function of the poset X and \[ A=\{(s,t,u,v)\in R\times D\times D\times R| \quad s\leq t,\quad u\leq v\}. \] From this, several useful corollaries are then easily obtained.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 05A10
zbMATH DE Number: 4085716
zbMATH Keywords: poset
zbMATH Keywords: subposet
zbMATH Keywords: Möbius function
reviewed by: J. Neggers
MaRDI profile type: Publication
cites work: On the foundations of combinatorial theory I. Theory of M�bius Functions
description: scientific article; zbMATH DE number 4085716