A single-element extension of antimatroids
type: Item
instance of: scholarly article
title: A single-element extension of antimatroids
zbMATH Open document ID: 1001.05035
DOI: 10.1016/S0166-218X(01)00288-8
author: Masataka Nakamura
published in: Discrete Applied Mathematics
publication date: 2002-08-29T00:00:00Z
review text: An ``antimatroid'' is a finite set together with a closure operator which satisfies the ``anti-exchange property.'' (Closure operators of matroids satisfy the ``exchange property.'' The definition used in this paper is based on the set of complements of closed sets of the antimatroid.) Let \(\mathcal A\) be an antimatroid on \(E\), \(p \in E\), and \(\mathcal B\) the antimatroid on \(E \setminus \{p\}\) obtained by ``reduction'' (sometimes called ``deletion'') of \(p\). The operation of retrieving \(\mathcal A\) by using the structure of \(\mathcal B\) and certain additional information is termed a ``lifting.'' The paper distinguishes two types of liftings and shows that this dichotomy can be used to characterize the edge-shelling antimatroids of trees and the poset-shelling antimatroids.
Mathematics Subject Classification ID: 05B35
zbMATH DE Number: 1792320
zbMATH Keywords: antimatroid
zbMATH Keywords: edge-shellings of trees
zbMATH Keywords: poset shelling
reviewed by: James F. Lawrence
MaRDI profile type: Publication
cites work: Matroids and antimatroids - a survey
cites work: The theory of convex geometries
full work available at URL: s0166-218x(01)00288-8
OpenAlex ID: W2057160898
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description: scientific article; zbMATH DE number 1792320