A Geometric Characterization of Poly-antimatroids

Yulia Kempner; Vadim E. Levit

doi:10.1016/j.endm.2007.01.050

A Geometric Characterization of Poly-antimatroids

Yulia Kempner, Vadim E. Levit

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

The concept of "antimatroid with repetition" was coined by Bjorner, Lovasz and Shor in 1991 as an extension of the notion of antimatroid in the framework of non-simple languages [Björner A., L. Lovász, and P. R. Shor, Chip-firing games on graphs, European Journal of Combinatorics 12 (1991), 283-291]. There are some equivalent ways to define antimatroids. They may be separated into two categories: antimatroids defined as set systems and antimatroids defined as languages. For poly-antimatroids we use the set system approach. In this research we concentrate on interrelations between geometric, algorithmic, and lattice properties of poly-antimatroids. Much to our surprise it turned out that even the two-dimensional case is not trivial.

Original language	English
Pages (from-to)	357-364
Number of pages	8
Journal	Electronic Notes in Discrete Mathematics
Volume	28
DOIs	https://doi.org/10.1016/j.endm.2007.01.050
State	Published - 1 Mar 2007

Keywords

Abstract convexity
multiset
poly-antimatroid

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10.1016/j.endm.2007.01.050

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A Geometric Characterization of Poly-antimatroids

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