On zero-sum turan problems of Bialostocki and Dierker
نویسندگان
چکیده
منابع مشابه
On Zero - Sum Problems
Let G be an additive abelian group. The zero-sum problem for G asks for the least positive integer k such that for any a1, · · · , ak ∈ G there is an I ⊆ {1, · · · , k} of required cardinality satisfying ∑ i∈I ai = 0. In this talk we will introduce the famous theorem of P. Erdős, A. Ginzburg and A. Ziv (for G = Zn), and recent results of L. Rónya on the Kemnitz conjecture concerning the group Z...
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For a graph G whose number of edges is divisible by k, let R(G,Zk) denote the minimum integer r such that for every function f : E(Kr) 7→ Zk there is a copy G′ of G in Kr so that ∑ e∈E(G′) f(e) = 0 (in Zk). We prove that for every integer k, R(Kn, Zk) ≤ n + O(k log k) provided n is sufficiently large as a function of k and k divides ( n 2 ) . If, in addition, k is an odd prime-power then R(Kn, ...
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A prototype of zero–sum theorems, the well–known theorem of Erdős, Ginzburg and Ziv says that for any positive integer n, any sequence a1, a2, · · · , a2n−1 of 2n − 1 integers has a subsequence of n elements whose sum is 0 modulo n. Appropriate generalizations of the question, especially that for (Z/pZ), generated a lot of research and still have challenging open questions. Here we propose a ne...
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— In this article, we study the maximal cross number of long zero-sumfree sequences in a finite Abelian group. Regarding this inverse-type problem, we formulate a general conjecture and prove, among other results, that this conjecture holds true for finite cyclic groups, finite Abelian p-groups and for finite Abelian groups of rank two. Also, the results obtained here enable us to improve, via ...
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This is a survey of recent advances on zero-sum problems and Snevily’s conjecture concerning finite abelian groups. In particular, we will introduce Reiher’s recent solution to the Kemnitz conjecture and our simplification. 1. On Zero-sum Problems The theory of zero-sums began with the following celebrated theorem. The Erdős-Ginzburg-Ziv Theorem [Bull. Research Council. Israel, 1961]. For any c...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1992
ISSN: 0263-6115
DOI: 10.1017/s1446788700036569