{"?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-4NV94BIZ/ef8f78f9-a903-467e-b263-b89e420cd901/PDF","dcterms:extent":"445 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4NV94BIZ/097e8f1b-9b2b-41fa-9210-e9dbc4a886a1/TEXT","dcterms:extent":"65 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-4NV94BIZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Costa, Simone","Pasotti, Anita","Pellegrini, Marco Antonio"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 241-271"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:40648195","URN:URN:NBN:SI:doc-4NV94BIZ"],"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":"biembedding"},{"@xml:lang":"sl","#text":"bivložitev"},{"@xml:lang":"en","#text":"Heffter array"},{"@xml:lang":"sl","#text":"Heffterjeva matrika"},{"@xml:lang":"en","#text":"multipartite complete graph"},{"@xml:lang":"sl","#text":"polni večdelni graf"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Relative Heffter arrays and biembeddings|"},"dc:description":[{"@xml:lang":"sl","#text":"Relative Heffter arrays, denoted by ?$\\mathrm{H}_t(m,n; s,k)$?, have been introduced as a generalization of the classical concept of Heffter array. A ?$\\mathrm{H}_t(m,n; s,k)$? is an ?$m\\times n$? partially filled array with elements in ?$\\mathbb{Z}_v$?, where ?$v=2nk+t$?, whose rows contain ?$s$? filled cells and whose columns contain ?$k$? filled cells, such that the elements in every row and column sum to zero and, for every ?$x\\in \\mathbb{Z}_v$? not belonging to the subgroup of order ?$t$?, either ?$x$? or ?$-x$? appears in the array. In this paper we show how relative Heffter arrays can be used to construct biembeddings of cyclic cycle decompositions of the complete multipartite graph ?$K_{\\frac{2nk+t}{t}\\times t}$? into an orientable surface. In particular, we construct such biembeddings providing integer globally simple square relative Heffter arrays for ?$t=k=3,5,7,9$? and ?$n\\equiv 3 \\pmod 4$? and for ?$k=3$? with ?$t=n,2n$?, any odd ?$n$?"},{"@xml:lang":"sl","#text":"Relativne Heffterjeve matrike, označene z ?$\\mathrm{H}_t(m,n; s,k)$?, so bile vpeljane kot posplošitev klasičnega koncepta Heffterjeve matrike. ?$\\mathrm{H}_t(m,n; s,k)$? je delno urejena matrika velikosti ?$m\\times n$? z elementi v ?$\\mathbb{Z}_v$?, kjer je ?$v=2nk+t$?, katere vrstice vsebujejo ?$s$? zapolnjenih celic in katere stolpci vsebujejo ?$k$? zapolnjenih celic, pri čemer je vsota elementov v vsaki vrstici in stolpcu enaka nič, in pri čemer se, za vsak ?$x\\in \\mathbb{Z}_v$?, ki ne pripada podgrupi reda ?$t$?, v matriki pojavi bodisi ?$x$? bodisi ?$-x$?. V članku pokažemo, kako s pomočjo relativnih Heffterjevih matrik konstruiramo bivložitve cikličnih cikelnih razgradenj polnega večdelnega grafa ?$K_{\\frac{2nk+t}{t}\\times t}$? na orientabilno ploskev. Posebej konstruiramo takšne bivložitve in predstavimo celoštevilske globalno enostavne kvadratne relativne Heffterjeve matrike za ?$t=k=3,5,7,9$? and ?$n\\equiv 3 \\pmod 4$? in za ?$k=3$?, kjer je ?$t=n,2n$?, za vsak lih ?$n$?"}],"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-4NV94BIZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-4NV94BIZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-4NV94BIZ/ef8f78f9-a903-467e-b263-b89e420cd901/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-4NV94BIZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-4NV94BIZ"}}}}