Israel Journal of Mathematics

, Volume 192, Issue 1, pp 143–156

Partitions of nonzero elements of a finite field into pairs

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Abstract

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.

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Copyright information

© Hebrew University Magnes Press 2012

Authors and Affiliations

  1. 1.Department of MathematicsMoscow Institute of Physics and TechnologyDolgoprudnyRussia
  2. 2.Discrete and Computational Geometry LaboratoryYaroslavl’ State UniversityYaroslavl’Russia
  3. 3.Saint-Petersburg Department of the Steklov MathematicalSaint-PetersburgRussia

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