Distributive Lattice Polyhedra

Yulia Kempner, Vadim E. Levit

Research output: Contribution to journalArticlepeer-review


Poly-antimatroids are generalization of the notion of antimatroid to multisets. When the underlying set consists of only two elements, such two-dimensional poly-antimatroids correspond to point sets in the integer lattice Zd. In this research we concentrate on geometrical properties of two-dimensional poly-antimatroids and prove that these sets form distributive lattice polyhedra. Our findings imply that two-dimensional poly-antimatroids have convex dimension 2. Further we investigate geometrical properties of three-dimensional distributive lattice polyhedra.

Original languageEnglish
Pages (from-to)483-487
Number of pages5
JournalElectronic Notes in Discrete Mathematics
StatePublished - 1 Aug 2009
Externally publishedYes


  • Antimatroid
  • convex dimension
  • distributive lattice
  • polyomino


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