{"?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-BC8FDUQA/76135338-0bf1-4a3b-b952-39ccb505c864/PDF","dcterms:extent":"416 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-BC8FDUQA/1c01d269-d535-445d-877c-76d78525b1c3/TEXT","dcterms:extent":"62 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-BC8FDUQA","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":"Goff, Michael","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"str. 45-66"}],"dc:identifier":["COBISSID:17732953","ISSN:1855-3966","URN:URN:NBN:SI:doc-BC8FDUQA"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"combinatorial species"},{"@xml:lang":"en","#text":"complete multipartite graph"},{"@xml:lang":"en","#text":"distinguishing partition"},{"@xml:lang":"sl","#text":"kombinatorične vrste"},{"@xml:lang":"sl","#text":"polni multipartitni graf"},{"@xml:lang":"sl","#text":"preštevanje dreves"},{"@xml:lang":"sl","#text":"razlikovalna particija"},{"@xml:lang":"en","#text":"tree enumeration"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Distinguishing partitions of complete multipartite graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A distinguishing partition of a set ?$X$? with automorphism group ?$\\text{aut}(X)$? is a partition of ?$X$? that is fixed by no nontrivial element of ?$\\text{aut}(X)$?. In the event that ?$X$? is a complete multipartite graph with its automorphism group, the existence of a distinguishing partition is equivalent to the existence of an asymmetric hypergraph with prescribed edge sizes. An asymptotic result is proven on the existence of a distinguishing partition when ?$X$? is a complete multipartite graph with ?$m_1$? parts of size ?$n_1$? and ?$m_2$? parts of size ?$n_2$? for small ?$n_1$?, ?$m_2$? and large ?$m_1$?, ?$n_2$?. A key tool in making the estimate is counting the number of trees of particular classes"},{"@xml:lang":"sl","#text":"Razlikovalna particija množice ?$X$? z grupo avtomorfizmov ?$\\text{aut}(X)$? je particija množice ?$X$?, ki je ne ohranja noben netrivialen element ?$\\text{aut}(X)$?. V primeru, ko je ?$X$? polni multipartitni graf, ?$\\text{aut}(X)$? pa grupa vseh njegovih avtomorfizmov, je obstoj razlikovalne particije ekvivalenten obstoju asimetričnega hipergrafa s predpisanimi velikostmi povezav. Dokažemo asimptotski rezultat o obstoju razlikovalne particije, ko je ?$X$? polni multipartitni graf z ?$m_1$? deli velikosti ?$n_1$? in ?$m_2$? deli velikosti ?$n_2$? za majhne ?$n_1$?, ?$m_2$? in velike ?$m_1$?, ?$n_2$?. Ključno orodje pri ocenjevanju je preštevanje dreves določenih razredov"}],"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-BC8FDUQA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-BC8FDUQA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-BC8FDUQA/76135338-0bf1-4a3b-b952-39ccb505c864/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-BC8FDUQA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-BC8FDUQA"}}}}