272 KB21 KB200820252014Kempner, YuliaLevit, Vadim E.številka:1letnik:7str. 73-82COBISSID:16793177ISSN:1855-3966URN:URN:NBN:SI:doc-5FQG3FNZenDruštvo matematikov, fizikov in astronomov SlovenijeArs mathematica contemporaneaantimatroidconvex dimensionkombinatorikalattice animalmatematikapolyhedronpolyominoPoly-antimatroid polyhedra|The notion of "antimatroid with repetition" was conceived by Bjorner, Lovasz and Shor in 1991 as an extension of the notion of antimatroid in the framework of non-simple languages. Further they were investigated by the name of "poly-antimatroids" (Nakamura, 2005, Kempner and Levit, 2007), where the set system approach was used. If the underlying set of a poly-antimatroid consists of n elements, then the poly-antimatroid may be represented as a subset of the integer lattice ?$\mathbb{Z}^n$?. We concentrate on geometrical properties of two-dimensional ?$(n = 2)$? poly-antimatroids - poly-antimatroid polygons, and prove that these polygons are parallelogram polyominoes. We also show that each two-dimensional poly-antimatroid is a poset poly-antimatroid, i.e., it is closed under intersection. 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 ?$n$?TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije