Israel Journal of Mathematics

, Volume 182, Issue 1, pp 505–508 | Cite as

A proof of snevily’s conjecture

Article

Abstract

We prove Snevily’s conjecture, which states that for any positive integer k and any two k-element subsets {a 1, …, a k } and {b 1, …, b k } of a finite abelian group of odd order there exists a permutation πS k such that all sums a i + b π(i) (i ∈ [1, k]) are pairwise distinct.

Keywords

Positive Integer Vector Space Induction Hypothesis Formal Variable Symmetric Group 
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References

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    N. Alon, Additive Latin transversals, Israel Journal of Mathematics 117 (2000), 125–130.CrossRefMATHMathSciNetGoogle Scholar
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    S. Dasgupta, Gy. Károlyi, O. Serra and B. Szegedy, Transversals of additive Latin squares, Israel Journal of Mathematics 126 (2001), 17–28.CrossRefMATHMathSciNetGoogle Scholar
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    H. Snevily, Unsolved Problems: The Cayley Addition Table of ℤ/nℤ, American Mathematical Monthly 106 (1999), 584–585.CrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University Magnes Press 2011

Authors and Affiliations

  1. 1.Nova International SchoolsSkopjeMacedonia

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