On D-complementation
type: Item
instance of: scholarly article
title: On D-complementation
zbMATH Open document ID: 0546.05020
DOI: 10.1016/0001-8708(84)90008-2
published in: Advances in Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In a distributive lattice D, an order isomorphism \(\gamma\) is given from the join-irreducible elements to the meet-irreducible elements, and is extended to a bijection of D, called D-complementation. Some examples and results are given in the case where D is D(P), the set of descending subsets (or, equivalently, antichains) of a partially ordered set P. The results are then used to define a generalization of a matroid on a poset, in which the map \(\gamma\) in D(D(P)) gives the bases from the circuits and the hyperplanes from the bases.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 06D05
zbMATH DE Number: 3869349
zbMATH Keywords: lattice complementation
zbMATH Keywords: matroid axiomatization. Peoli, Luig
MaRDI profile type: Publication
full work available at URL: 0001-8708(84)90008-2
OpenAlex ID: W2094318292
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description: scientific article; zbMATH DE number 3869349