A Geometric Characterization of Poly-antimatroids

Yulia Kempner, Vadim E. Levit

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish
Pages (from-to)357-364
Number of pages8
JournalElectronic Notes in Discrete Mathematics
StatePublished - 1 Mar 2007
Externally publishedYes


  • Abstract convexity
  • multiset
  • poly-antimatroid


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