A single-element extension of antimatroids
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.
scientific article; zbMATH DE number 1792320