{"?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-Q3AB3JIV/c4b6c558-1298-4416-8b7d-3dc63aceab9a/PDF","dcterms:extent":"306 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Q3AB3JIV/12455d5e-eaeb-4cf5-8443-b4a7b504d55e/TEXT","dcterms:extent":"32 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-Q3AB3JIV","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Dinitz, Jeffrey H.","Wanless, Ian M."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 81-93"}],"dc:identifier":["COBISSID:18174553","ISSN:1855-3966","URN:URN:NBN:SI:doc-Q3AB3JIV"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"dvojna vložitev"},{"@xml:lang":"sl","#text":"Heffterjeva matrika"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The existence of square integer Heffter arrays|"},"dc:description":[{"@xml:lang":"sl","#text":"An integer Heffter array ?$H(m, n; s, t)$? is an ?$m \\times n$? partially filled matrix with entries from the set ?$\\{\\pm 1, \\pm 2, \\dots , \\pm ms\\}$? such that i) each row contains ?$s$? filled cells and each column contains ?$t$? filled cells, ii) every row and column sums to 0 (in ?$\\mathbb{Z}$?), and iii) no two entries agree in absolute value. Heffter arrays are useful for embedding the complete graph ?$K_{2ms+1}$? on an orientable surface in such a way that each edge lies between a face bounded by an ?$s$?-cycle and a face bounded by a ?$t$?-cycle. In 2015, Archdeacon, Dinitz, Donovan and Yazici constructed square (i.e. ?$m=n$?) integer Heffter arrays for many congruence classes. In this paper we construct square integer Heffter arrays for all the cases not found in that paper, completely solving the existence problem for square integer Heffter arrays"},{"@xml:lang":"sl","#text":"Celoštevilska Heffterjeva matrika ?$H(m, n; s, t)$? je ?$m \\times n$? delno zapolnjena matrika z elementi iz množice ?$\\{\\pm 1, \\pm 2, \\dots , \\pm ms\\}$? tako da i) vsaka vrstica vsebuje ?$s$? zapolnjenih polj in vsak stolpec vsebuje ?$t$? zapolnjenih polj, ii) vsota elementov v vsaki vrstici in vsakem stolpcu je enaka nič (v ?$\\mathbb{Z}$?), in iii) nobena dva elementa nimata enake absolutne vrednosti. Heffterjeve matrike so koristne pri vlaganju polnega grafa ?$K_{2ms+1}$? na orientabilno ploskev tako da vsaka povezava leži med nekim licem omejenim z ?$s$?-ciklom in nekim licem omejenim s ?$t$?-ciklom. Leta 2015 so Archdeacon, Dinitz, Donovan in Yazici konstruirali kvadratne (tj.?$m=n$?) celoštevilske Heffterjeve matrike za mnoge kongruenčne razrede. V članku konstruiramo kvadratne celoštevilske Heffterjeve matrike za vse primere, ki jih Archdeacon, Dinitz, Donovan in Yazici v svojem članku niso obravnavali, in popolnoma rešimo problem obstoja za kvadratne celoštevilske Heffterjeve matrike"}],"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-Q3AB3JIV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-Q3AB3JIV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-Q3AB3JIV/c4b6c558-1298-4416-8b7d-3dc63aceab9a/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-Q3AB3JIV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-Q3AB3JIV"}}}}