Add to ORKGLet $G$ be a finite abelian group. A nonempty subset $A$ in $G$ is called a basis of order $h$ if $hA=G$; when $hA \neq G$, it is called a nonbasis of order $h$. Our interest is in all possible sizes of $hA$ when $A$ is a nonbasis of order $h$ in $G$ of maximum size; we provide the complete answer when $h=2$ or $h=3$
Sum-avoiding sets in groups, Discrete Analysis 2016:15, 27 pp. Let $A$ be a subset of an Abelian gr...
AbstractWe give a closed formula for the minimal sumset size function μG(r,s)=min{|A+B|:A,B⊂G,|A|=r,...
AbstractLet G be a finite abelian group of order g. We determine, for all 1⩽r,s⩽g, the minimal size ...
For a non-empty $k$-element set $A$ of an additive abelian group $G$ and a positive integer $r \leq ...
AbstractWe survey the state of research to determine the maximum size of a nonspanning subset of a f...
We survey the state of research to determine the maximum size of a nonspanning subset of a finite ab...
AbstractLet G be a group written additively and let A denote a set of nonzero elements of G. The sma...
AbstractLetGbe an abelian group containing a finite subsetBsuch that, for every non-empty finite sub...
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
AbstractGiven a group G and positive integers r,s≤|G|, we denote by μG(r,s) the least possible size ...
A family $\mathcal{F}\subset 2^G$ of subsets of an abelian group $G$ is a Sidon system if the sumset...
Let G be a finite abelian group, and let S µ G be a subset of distinct nonzero elements of G. If eac...
AbstractLet h ≥ 2 be any integer, let c = h(1 + 2−1h)h − 1. In this paper, it is proved that every f...
Abstract. In this paper we study sum-free sets of order m in finite Abelian groups. We prove a gener...
Let G be a group and S a non-empty subset of G. If ab∉S for any a,b∈S, then S is called sum-free. We...
Sum-avoiding sets in groups, Discrete Analysis 2016:15, 27 pp. Let $A$ be a subset of an Abelian gr...
AbstractWe give a closed formula for the minimal sumset size function μG(r,s)=min{|A+B|:A,B⊂G,|A|=r,...
AbstractLet G be a finite abelian group of order g. We determine, for all 1⩽r,s⩽g, the minimal size ...
For a non-empty $k$-element set $A$ of an additive abelian group $G$ and a positive integer $r \leq ...
AbstractWe survey the state of research to determine the maximum size of a nonspanning subset of a f...
We survey the state of research to determine the maximum size of a nonspanning subset of a finite ab...
AbstractLet G be a group written additively and let A denote a set of nonzero elements of G. The sma...
AbstractLetGbe an abelian group containing a finite subsetBsuch that, for every non-empty finite sub...
AbstractLet G be a group. We study the minimal sumset (or product set) size μG(r,s)=min{|A⋅B|}, wher...
AbstractGiven a group G and positive integers r,s≤|G|, we denote by μG(r,s) the least possible size ...
A family $\mathcal{F}\subset 2^G$ of subsets of an abelian group $G$ is a Sidon system if the sumset...
Let G be a finite abelian group, and let S µ G be a subset of distinct nonzero elements of G. If eac...
AbstractLet h ≥ 2 be any integer, let c = h(1 + 2−1h)h − 1. In this paper, it is proved that every f...
Abstract. In this paper we study sum-free sets of order m in finite Abelian groups. We prove a gener...
Let G be a group and S a non-empty subset of G. If ab∉S for any a,b∈S, then S is called sum-free. We...
Sum-avoiding sets in groups, Discrete Analysis 2016:15, 27 pp. Let $A$ be a subset of an Abelian gr...
AbstractWe give a closed formula for the minimal sumset size function μG(r,s)=min{|A+B|:A,B⊂G,|A|=r,...
AbstractLet G be a finite abelian group of order g. We determine, for all 1⩽r,s⩽g, the minimal size ...