| Naslov: | Finding a perfect matching of F_2^n with prescribed differences |
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| Avtorji: | ID Kovács, Benedek (Avtor) |
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| Datoteke: |  AMC_Kovacs_2026.pdf (467,06 KB)
MD5: 8FFDD2BEE697ABEAA3D3E4A466F79281
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | ZUP - Založba Univerze na Primorskem
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| Opis: | We consider the following question by Balister, Győri and Schelp: given 2^{n-1} nonzero vectors in F_2^n with zero sum, is it always possible to partition the elements of F_2^n 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 F_p, 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 F_2^n 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+ε of the given vectors are equal (for all ε>0 and n sufficiently large based on ε). |
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| Ključne besede: | binary vector spaces, seating couples, prescribed differences, perfect matching, functional batch code, graph colourings |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 20.11.2025 |
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| Založnik: | Založba Univerze na Primorskem |
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| Leto izida: | 2026 |
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| Št. strani: | 22 str. |
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| Številčenje: | Vol. 26, no. 1, [article no.] P1.05 |
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| PID: | 20.500.12556/RUP-22289  |
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| UDK: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3265.91b |
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| Datum objave v RUP: | 21.12.2025 |
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| Število ogledov: | 221 |
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| Število prenosov: | 0 |
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| Metapodatki: |    |
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