{"?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-L3PQEXJJ/9ab94e89-b52c-40d1-abe7-ab4dafcda892/PDF","dcterms:extent":"467 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-L3PQEXJJ/c4371467-58af-4b79-9c2b-e82ba852e03f/TEXT","dcterms:extent":"66 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-L3PQEXJJ/68156991-7440-4495-b7d2-77a384c9f895/PDF","dcterms:extent":"173 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-L3PQEXJJ/bdc54495-bfb0-4731-9390-1218d11af1ea/TEXT","dcterms:extent":"4 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-L3PQEXJJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":"Kovács, Benedek","dc:format":[{"@xml:lang":"sl","#text":"številka:1, article  p1.05"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-22"}],"dc:identifier":["DOI:10.26493/1855-3974.3265.91b","ISSN:1855-3974","COBISSID_HOST:288361987","URN:URN:NBN:SI:doc-L3PQEXJJ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:subject":[{"@xml:lang":"sl","#text":"barvanje grafov"},{"@xml:lang":"sl","#text":"binarni vektorski prostori"},{"@xml:lang":"en","#text":"binary vector spaces"},{"@xml:lang":"sl","#text":"določene razlike"},{"@xml:lang":"sl","#text":"fukcionalna paketna koda"},{"@xml:lang":"en","#text":"functional batch code"},{"@xml:lang":"en","#text":"graph colourings"},{"@xml:lang":"en","#text":"perfect matching"},{"@xml:lang":"sl","#text":"popolno prirejanje"},{"@xml:lang":"en","#text":"prescribed differences"},{"@xml:lang":"sl","#text":"razporeditev parov"},{"@xml:lang":"en","#text":"seating couples"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Finding a perfect matching of F2/n with prescribed differences|"},"dc:description":[{"@xml:lang":"sl","#text":"We consider the following question by Balister, Győri and Schelp: given 2n-1 nonzero vectors in F2n with zero sum, is it always possible to partition the elements of F2n into pairs such that the difference between the two elements of the i-th pair is equal to the i-th given vector for every i? An analogous question in Fp, which is a case of the so-called \"seating couples\" problem, has been resolved by Preissmann and Mischler in 2009. In this paper, we prove the conjecture in F2n in the case when the number of distinct values among the given difference vectors is at most n-2log(n)-1, and also in the case when at least a fraction 1/2+? of the given vectors are equal (for all ?>0 and n sufficiently large based on ?)"},{"@xml:lang":"sl","#text":"Obravnavamo naslednje vprašanje, ki so ga postavili Balister, Győri in Schelp: Dano je 2n-1 ničelnih vektorjev v Fn 2 z ničelno vsoto. Ali je vedno mogoče razdeliti elemente množice Fn 2 v pare tako, da je razlika med dvema elementoma v i-tem paru enaka i-temu danemu vektorju za vsak i? Analogno vprašanje v Fp, ki je primer tako imenovanega problema »razporeditve parov«, sta rešila Preissmann in Mischler leta 2009. V tem članku dokazujemo domnevo v Fn 2 v primeru, ko je število različnih vrednosti med danimi vektorji razlik največ n - 2 log n - 1, ter tudi v primeru, ko je vsaj delež 1 2 + ? danih vektorjev enak (za vse ? > 0 in dovolj velik n glede na ?)"}],"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-L3PQEXJJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-L3PQEXJJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-L3PQEXJJ/9ab94e89-b52c-40d1-abe7-ab4dafcda892/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-L3PQEXJJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-L3PQEXJJ"}}}}