Finding a perfect matching of $\mathbb{F}_2^n$ with prescribed differences
We consider the following question by Balister, Gy\H{o}ri and Schelp: given $2^{n-1}$ nonzero vectors in $\mathbb{F}_2^n$ with zero sum, is it always possible to partition the elements of $\mathbb{F}_2^n$ into pairs such that the difference between the two elements of the $i$-th pair is equal to the...
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