Height and semimodularity in finite 0,1-posets
type: Item
instance of: scholarly article
title: Height and semimodularity in finite 0,1-posets
zbMATH Open document ID: 0629.06003
author: J. Nieminen
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1987-01-01T00:00:00Z
review text: Let P be a finite poset with 0 and 1. \(a\vee b\) is a freely chosen minimal upper bound of a and b. \(a\wedge b\) is defined dually. (L;\(\vee,\wedge)\) is called a \(\chi\)-lattice derived from P. h(a) denotes the length of a longest maximal chain between 0 and a. A concept of semimodularity is defined so that \(h(a)+h(b)\geq h(a\vee b)+h(a\wedge b)\) holds in any \(\chi\)-lattice derived from P.
Mathematics Subject Classification ID: 06A06
Mathematics Subject Classification ID: 06C10
zbMATH DE Number: 4023344
zbMATH Keywords: finite poset
zbMATH Keywords: \(\chi \)-lattice
zbMATH Keywords: length
zbMATH Keywords: maximal chain
zbMATH Keywords: semimodularity
reviewed by: Tamás Schmidt
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4023344