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On a generalization of the seating couples problem. (English) Zbl 1343.05030

Summary: We prove a conjecture of Adamaszek generalizing the seating couples problem to the case of \(2n\) seats. Concretely, we prove that given a positive integer \(n\) and \(d_1,\ldots, d_n \in(\mathbb{Z}/2n)^\times\) we can partition \(\mathbb{Z}/2n\) into \(n\) pairs with differences \(d_1, \ldots, d_n\).

MSC:

05A17 Combinatorial aspects of partitions of integers
05A15 Exact enumeration problems, generating functions
11A41 Primes
11B75 Other combinatorial number theory
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References:

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