467 KB66 KB173 KB4 KB200820262026Kovács, Benedekštevilka:1, article p1.05letnik:26str. 1-22DOI:10.26493/1855-3974.3265.91bISSN:1855-3974COBISSID_HOST:288361987URN:URN:NBN:SI:doc-L3PQEXJJenUniverza na PrimorskemArs mathematica contemporaneabarvanje grafovbinarni vektorski prostoribinary vector spacesdoločene razlikefukcionalna paketna kodafunctional batch codegraph colouringsperfect matchingpopolno prirejanjeprescribed differencesrazporeditev parovseating couplesFinding a perfect matching of F2/n with prescribed differences|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 ?)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 ?)TEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije