Kohen, Daniel; Sadofschi Costa, Iván On a generalization of the seating couples problem. (English) Zbl 1343.05030 Discrete Math. 339, No. 12, 3017-3019 (2016). 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 \(d_1, \ldots, d_n\). Cited in 3 Documents MSC: 05A17 Combinatorial aspects of partitions of integers 05A15 Exact enumeration problems, generating functions 11A41 Primes 11B75 Other combinatorial number theory Keywords:seating; couples; Cauchy-Davenport theorem; partition; sumset PDFBibTeX XMLCite \textit{D. Kohen} and \textit{I. Sadofschi Costa}, Discrete Math. 339, No. 12, 3017--3019 (2016; Zbl 1343.05030) Full Text: DOI arXiv References: [1] Chowla, I., A theorem on the addition of residue classes: application to the number \(\Gamma(k)\) in Waring’s problem, Q. J. Math., os-8, 1, 99-102 (1937) · JFM 63.0128.02 [2] Hall, M., A combinatorial problem on abelian groups, Proc. Amer. Math. Soc., 3, 584-587 (1952) · Zbl 0047.02701 [3] Karasev, R. N.; Petrov, F. V., Partitions of nonzero elements of a finite field into pairs, Israel J. Math., 192, 1, 143-156 (2012) · Zbl 1287.11015 [4] Kohen, D.; Sadofschi, I., A new approach on the seating couples problem · Zbl 1343.05030 [5] Mezei, T. R., Seating couples and Tic-Tac-Toe (2013), Eötvös Loránd University, (Master’s thesis) [6] Preissmann, E.; Mischler, M., Seating couples around the King’s table and a new characterization of prime numbers, Amer. Math. Monthly, 116, 3, 268-272 (2009) · Zbl 1228.05039 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.