19-25 June 2011
Bled, Slovenia
Europe/Ljubljana timezone
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Poly-Antimatroid Polyhedra

Presented by Dr. Yulia KEMPNER
Type: Oral presentation
Track: General session


A poly-antimatroid is a finite non-empty multiset system that satisfies the basic antimatroid properties. If the underlying set of a poly-antimatroid consists of n elements, then it can be represented as a subset of the n-dimensional integer lattice. Firstly, we focus on geometrical properties of two-dimensional poly-antimatroids (n=2), and prove that they are, actually, polygons known in enumerative combinatorics as parallelogram polyominoes. In addition, we show that each two-dimensional poly-antimatroid is a poset poly-antimatroid, i.e., it is closed under intersection. Secondly, we recall that the convex dimension cdim(S) of a poly-antimatroid S is the minimum number of maximal chains needed to realize S. While the convex dimension of an n-dimensional poly-antimatroid may be arbitrarily large, we prove that the convex dimension of an n-dimensional poset poly-antimatroid is equal to n.


Location: Bled, Slovenia
Address: Best Western Hotel Kompas Bled

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