Let $\\mathscr{M}_{(2,1)}(N)$ be the infimum of the largest sum-free subset of\nany set of $N$ positive integers. An old conjecture in additive combinatorics\nasserts that there is a constant $c=c(2,1)$ and a function $\\omega(N)o\\infty$\nas $No\\infty$, such that $...
A subset A of a given finite abelian group G is called (k,l)-sum-free if the sum of k (not necessarily distinct) elements of A does not equal the sum of l (not necessarily distinct) elements of A. We are interested in finding the maximum size u03bbk,l(G) of a (k,l)-sum-...
LetA be a subset of an abelian groupG with |G|=n. We say thatA is sum-free if there do not existx, y, z εA withx+y=z. We determine, for anyG, the maxi
On the maximum size of a $(k,l)$-sum-free subset of an abelian group Bela Bajnok Full-Text Cite this paper Add to My Lib Abstract: A subset $A$ of a given finite abelian group $G$ is called $(k,l)$-sum-free if the sum of $k$ (not necessarily distinct) elements of $A...
Let $p$ be a sufficiently large prime and $\\\mathcal{A}$ be a sum-free subset of $\\\mathbb{Z}\\\slash p\\\mathbb{Z}$; improving on a previous result of V. F. Lev, we show that if $|\\\mathcal{A}|=extup{card}(\\\mathcal{A}) > 0.324 p$, then $\\\mathcal{A...
摘要: Let be a finite abelian group and be a subset of . Let denote the set of group elements which can be expressed as a sum of a nonempty subset of . We say that is zero-sum free if . In this talk, we introduce the problem of determining the provided that is a zero-sum free...
Let $G$ be a finite additively written abelian group, and let $X$ be a subset of 7 elements in $G$. We show that if $X$ contains no nonempty subset with sum zero, then the number of the elements which can be expressed as the sum over a nonempty subsequence of $X$ is at least...
VF Lev, VF Lev - Israel Journal of Mathematics, 2006 - link.springer.com We notice that Lemmas 1-3 remain valid if A is a subset of Z/pZ (rather than B. Green and IZ Ruzsa,Sum-free sets in abelian groups, Israel Journal of Mathematics 147 (2005 KS Kedlaya,Product-free subsets of...
If A is sum-full, then it is not zero-sum-free; that is, if every element of A is representable as a sum of two other elements, then A has a nonempty zero-sum subset. The proof of Theorem 1 is of combinatorial nature; it is both surprisingly short and elementary, requiring nothing...
A subset S of an additive group G is called a maximal sum-free set in G if (S+S) S = ø and ∣S∣ ≥∣T∣ for every sum-free set T in G. It is shown that if G is an elementary abelian p–group of order pn, where p = 3k ± 1, then a maximal sum-free set in...