Geometry of poset antimatroids

Yulia Kempner, Vadim E. Levit

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


An antimatroid is an accessible set system closed under union. A poset antimatroid is a particular case of antimatroid, which is formed by the lower sets of a poset. Feasible sets in a poset antimatroid ordered by inclusion form a distributive lattice, and every distributive lattice can be formed in this way. We introduce the polydimension of an antimatroid as the minimum dimension d such that the antimatroid may be isometrically embedded into d-dimensional integer lattice Zd. We prove that every antimatroid of poly-dimension 2 is a poset antimatroid, and demonstrate both graph and geometric characterizations of such antimatroids. Finally, a conjecture concerning poset antimatroids of arbitrary poly-dimension d is presented.

Original languageEnglish
Pages (from-to)169-173
Number of pages5
JournalElectronic Notes in Discrete Mathematics
StatePublished - 15 May 2013


  • Antimatroid
  • Dimension
  • Poset antimatroid


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