CD-independent subsets in meet-distributive lattices.
type: Item
instance of: scholarly article
title: CD-independent subsets in meet-distributive lattices.
zbMATH Open document ID: 1314.06011
author: Gábor Czédli
published in: Acta Mathematica Hungarica
publication date: 2014-08-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1307.0900
review text: For the notion of CD-independent subset in a distributive lattice, see \textit{G. Czédli, M. Hartmann, E. T. Schmidt} [Publ. Math. 74, No. 1-2, 127-134 (2009; Zbl 1199.06032)]. (These subsets are known also as laminar systems; see, e.g., \textit{P. P. Pach, G. Pluhár, A. Pongrácz, Cs. Szabó} [J. Math. Anal. Appl. 375, No. 1, 8-13 (2011; Zbl 1291.05020)].) In the paper under review, the main result of \textit{G. Czédli} et al. [loc. cit.] is generalised to meet-distributive lattices: it is proved that the size of a maximal CD-independent subset in a finite meet-distributive lattice does not exceed the number of atoms of the lattice plus its length. Some additional information on such subsets is obtained for several special subclasses of finite meet-distributive lattices. Another connection with the mentioned previous paper is through an application of CD-independent subsets: a new approach to counting islands on a rectangular board is developed.
reviewed by: Jānis Cīrulis
Mathematics Subject Classification ID: 06D05
Mathematics Subject Classification ID: 06C10
Mathematics Subject Classification ID: 05A15
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 6330508
zbMATH Keywords: CD-independent subsets
zbMATH Keywords: laminar systems
zbMATH Keywords: meet-distributive lattices
zbMATH Keywords: convex geometry of circles
zbMATH Keywords: numbers of islands
MaRDI profile type: Publication
OpenAlex ID: W1983958108
arXiv ID: 1307.0900
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DOI: 10.1007/S10474-013-0371-3
description: scientific article; zbMATH DE number 6330508