| Title: | Finding a perfect matching of F_2^n with prescribed differences |
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| Authors: | ID Kovács, Benedek (Author) |
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| Files: |  AMC_Kovacs_2026.pdf (467,06 KB)
MD5: 8FFDD2BEE697ABEAA3D3E4A466F79281
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| Abstract: | 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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| Keywords: | binary vector spaces, seating couples, prescribed differences, perfect matching, functional batch code, graph colourings |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 20.11.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2026 |
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| Number of pages: | 22 str. |
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| Numbering: | Vol. 26, no. 1, [article no.] P1.05 |
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| PID: | 20.500.12556/RUP-22289  |
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| UDC: | 51 |
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| eISSN: | 1855-3974 |
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| DOI: | 10.26493/1855-3974.3265.91b |
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| Publication date in RUP: | 21.12.2025 |
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| Views: | 207 |
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| Downloads: | 0 |
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