A new critical pair theorem applied to sum-free sets in Abelian groups

Yahya Ould Hamidoune, Alain Plagne

Type: Article

Publication Date: 2004-03-31

Citations: 30

DOI: https://doi.org/10.1007/s00014-003-0786-5

Abstract

We shall prove a new generalization of Vosper critical pair theorem to finite Abelian groups. We next apply this new tool to the theory of (k,l) -free sets in finite Abelian groups. In particular, in most cases, we describe the structure of maximal (k,l) -free sets and determine the maximal cardinality of such a set. This result allows us for instance to give precisions on an old result of Yap: we are able to describe completely the maximal sum-free sets with cardinality at least one third of that of the ambient group.

Locations

Commentarii Mathematici Helvetici - View - PDF

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+	Addition Theorems: The Addition Theorems of Group Theory and Number Theory	1976	Henry B. Mann
+ PDF Chat	Combinatorics: Room Squares, Sum-Free Sets, Hadamard Matrices	1972	W. D. Wallis Jennifer Wallis Anne Street
+	Theorie Algebrique des Nombres.	1971	R. A. Smith Pierre Samuel
+	Subsets with Small Sums in Abelian Groups' I: the Vosper Property	1997	Yahya Ould Hamidoune
+ PDF Chat	Maximal sum-free sets in finite abelian groups	1970	A. H. Rhemtulla Anne Street
+	Maximal sum-free sets in finite Abelian groups, III	1973	Hian-Poh Yap
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+ PDF Chat	A multiple set version of the $3k-3$ Theorem	2005	Yahya Ould Hamidoune Alain Plagne
+	Absch�tzung der asymptotischen Dichte von Summenmengen	1953	Martin Kneser