{"?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-108YTV0H/2725e9af-ad9c-42ed-afdb-8ab72ce92849/PDF","dcterms:extent":"417 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-108YTV0H/beb24b37-aa4c-4135-b0dd-f6de23611bf4/TEXT","dcterms:extent":"47 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-108YTV0H","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Cavenagh, Nicholas J.","Dinitz, Jeffrey H.","Donovan, Diane M.","Yazici, Emine Şule"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 369-395"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18956633","URN:URN:NBN:SI:doc-108YTV0H"],"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 cycle systems"},{"@xml:lang":"sl","#text":"bivložitveni ciklični sistemi"},{"@xml:lang":"en","#text":"Heffter arrays"},{"@xml:lang":"sl","#text":"Heffterjeve matrike"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The existence of square non-integer Heffter arrays|"},"dc:description":[{"@xml:lang":"sl","#text":"A Heffter array ?$H(n; k)$? is an ?$n \\times n$? matrix such that each row and column contains ?$k$? filled cells, each row and column sum is divisible by ?$2nk + 1$? and either ?$x$? or ?$-x$? appears in the array for each integer ?$1 \\leqslant x \\leqslant nk$?. Heffter arrays are useful for embedding the graph ?$K_{2nk + 1}$? on an orientable surface. An integer Heffter array is one in which each row and column sum is 0. Necessary and sufficient conditions (on ?$n$? and ?$k$?) for the existence of an integer Heffter array ?$H(n; k)$? were verified by D. S. Archdeacon et al. Des. Codes Cryptography 77, No. 2-3, 409-426 (2015) and J. H. Dinitz and I. M. Wanless Ars Math. Contemp. 13, No. 1, 81-93 (2017). In this paper we consider square Heffter arrays that are not necessarily integer. We show that such Heffter arrays exist whenever ?$3 \\leqslant k < n$?"},{"@xml:lang":"sl","#text":"Heffterjeva matrika ?$H(n; k)$? je ?$n \\times n$? matrika, v kateri vsaka vrstica in stolpec vsebuje ?$k$? zapolnjenih mest, vsaka vrstična in stolpčna vsota je deljiva z ?$2nk + 1$? in bodisi ?$x$? bodisi ?$-x$? nastopa v matriki za vsako celo število ?$1 \\leqslant x \\leqslant nk$?. Heffterjeve matrike so koristne pri vložitvi grafa ?$K_{2nk + 1}$? na orientabilno ploskev. Celoštevilska Heffterjeva matrika je takšna, pri kateri je vsota elementov vsake vrstice in stolpca enaka 0. Potrebne in zadostne pogoje (za ?$n$? in ?$k$?) za obstoj celoštevilske Heffterjeve matrike ?$H(n; k)$? so potrdili Archdeacon, Dinitz, Donovan in Yazici (2015) ter Dinitz in Wanless (2017). V članku obravnavamo kvadratne Heffterjeve matrike, ki niso nujno celoštevilske. Pokažemo, da takšne Heffterjeve matrike obstajajo vselej, kadar je ?$3 \\leqslant k < n$?"}],"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-108YTV0H","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-108YTV0H"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-108YTV0H/2725e9af-ad9c-42ed-afdb-8ab72ce92849/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-108YTV0H/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-108YTV0H"}}}}