Additive Latin transversals.
type: Item
instance of: scholarly article
title: Additive Latin transversals.
zbMATH Open document ID: 1047.11019
DOI: 10.1007/BF02773567
author: Noga Alon
published in: Israel Journal of Mathematics
publication date: 2000-01-01T00:00:00Z
review text: For \(p\) an odd prime the author proves that for any pair of sets \(A,B\subset\mathbb Z/p\mathbb Z\), if \(|A|=|B|\) there exists a bijection \(\phi\:A\to B\) such that the sums \(a+\phi(a)\) are pairwise distinct \((a\in A)\). The author uses the earlier given combinatorial Nullstellensatz [N. Alon, Combin. Probab. Comput. 8, No. 1-2, 7--29 (1999; Zbl 0920.05026)] to prove this. The author thus makes a first step toward a conjecture by Snevily (asserting that one can replace \(\mathbb Z/p\mathbb Z\) with any abelian group having odd order). Finally some extensions are given
reviewed by: Olaf Ninnemann
Mathematics Subject Classification ID: 11B75
Mathematics Subject Classification ID: 05B15
zbMATH DE Number: 1455691
MaRDI profile type: Publication
cites work: Combinatorial Nullstellensatz
cites work: Additive bases of vector spaces over prime fields
cites work: The polynomial method and restricted sums of congruence classes
cites work: Sumsets in vector spaces over finite fields
cites work: Has Every Latin Square of Order n a Partial Latin Transversal of Size n - 1?
cites work: Proof of a Conjecture by Dyson in the Statistical Theory of Energy Levels
cites work: Proof of a Conjecture by Dyson
cites work: A combinatorial proof of Dyson's conjecture
full work available at URL: https://doi.org/10.1007/bf02773567
OpenAlex ID: W2017299661
description: scientific article; zbMATH DE number 1455691