{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5FQG3FNZ/8ae7cffe-36c2-4cb2-b460-c633f357c4cf/PDF","dcterms:extent":"272 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5FQG3FNZ/e490e9fc-4898-4f58-af93-c0b612f2a024/TEXT","dcterms:extent":"21 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-5FQG3FNZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2014","dc:creator":["Kempner, Yulia","Levit, Vadim E."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 73-82"}],"dc:identifier":["COBISSID:16793177","ISSN:1855-3966","URN:URN:NBN:SI:doc-5FQG3FNZ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"antimatroid"},{"@xml:lang":"en","#text":"convex dimension"},{"@xml:lang":"sl","#text":"kombinatorika"},{"@xml:lang":"en","#text":"lattice animal"},{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"en","#text":"polyhedron"},{"@xml:lang":"en","#text":"polyomino"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Poly-antimatroid polyhedra|"},"dc:description":{"@xml:lang":"sl","#text":"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 ?$n$?"},"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-5FQG3FNZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-5FQG3FNZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-5FQG3FNZ/8ae7cffe-36c2-4cb2-b460-c633f357c4cf/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-5FQG3FNZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-5FQG3FNZ"}}}}