{"?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-ROW7W1J5/346E33CF-D00B-4101-B72B-1BE8CCC10EEF/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-ROW7W1J5/9d009de1-446f-49ca-b76d-516533608ed5/PDF","dcterms:extent":"309 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-ROW7W1J5/5417f820-f259-4804-9ca2-62b5ccd0e2eb/TEXT","dcterms:extent":"35 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-ROW7W1J5","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2011","dc:creator":["Ellingham, Mark N.","Schroeder, Justin Z."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:4"},{"@xml:lang":"sl","#text":"str. 111-123"}],"dc:identifier":["COBISSID:16264793","ISSN:1855-3966","URN:URN:NBN:SI:doc-ROW7W1J5"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"asymmetric uniform hypergraph"},{"@xml:lang":"en","#text":"complete equipartite graph"},{"@xml:lang":"en","#text":"distinguishing number"},{"@xml:lang":"en","#text":"distinguishing partition"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"sl","#text":"razlikovalna particija"},{"@xml:lang":"sl","#text":"razlikovalno število"},{"@xml:lang":"sl","#text":"teorija grafov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Distinguishing partitions and asymmetric uniform hypergraphs|"},"dc:description":{"@xml:lang":"sl","#text":"A distinguishing partition for an action of a group ?$\\Gamma$? on a set ?$X$? is a partition of ?$X$? that is preserved by no nontrivial element of ?$\\Gamma$?. As a special case, a distinguishing partition of a graph is a partition of the vertex set that is preserved by no nontrivial automorphism. In this paper we provide a link between distinguishing partitions of complete equipartite graphs and asymmetric uniform hypergraphs. Suppose that ?$m \\geq 1$? and ?$n \\geq 2$?. We show that an asymmetric ?$n$?-uniform hypergraph with ?$m$? edges exists if and only if ?$m \\geq f(n)$?, where ?$f(2) = f(14) = 6, f(6) = 5$?, and ?$f(n) = \\lfloor \\log_2 (n + 1) + 2 \\rfloor$? otherwise. It follows that a distinguishing partition of ?$K_{m(n)} = K_{n,n, \\dots ,n}$?, or equivalently for the wreath product action ?$S_n$? Wr ?$S_m$?, exists if and only if ?$m \\geq f(n)$?"},"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-ROW7W1J5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-ROW7W1J5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-ROW7W1J5/346E33CF-D00B-4101-B72B-1BE8CCC10EEF/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-ROW7W1J5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-ROW7W1J5"}}}}