Year: 2025
Type: article
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).
Author: Kovács, Benedek
Institution: Eötvös Loránd University
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1262964987
OpenAlex ID: W7126355510
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