Partitions of nonzero elements of a finite field into pairs
In this paper we prove that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives) in each pair. The algebraic and topological approaches to such problems are considered. We also give some generalizations of these results to packing translates in a finite or infinite field, and give a short proof of a particular case of the Eliahou-Kervaire-Plaigne theorem about sum-sets.
Unable to display preview. Download preview PDF.
- A. L. Cauchy, Recherches sur les nombres, Journal de l’École Polytechnique 9 (1813), 99–116.Google Scholar
- D. Kohen and I. Sadofschi, A new approach on the seating couples problem, http://arxiv.org/abs/1006.2571, 2010.
- R. Živaljević, Topological methods, in Handbook of Discrete and Computational Geometry (J. E. Goodman and J. O’Rourke, eds.), CRC, Boca Raton, 2004.Google Scholar