Add to ORKGA subset U of a group G is called k-universal if U contains a translate of every k-element subset of G. We give several nearly optimal constructions of small k-universal sets, and use them to resolve an old question of Erdős and Newman on bases for sets of integers, and to obtain several extensions for other groups.
Abstract. The word problem for discrete groups is well-known to be undecidable by a Turing Machine; ...
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Denote by d=d(G) and m=m(G), respectively, the smallest and the largest cardinality of a minimal gen...
It was proved by Banakh and Protasov that every group can be generated by a small set (in the sense ...
Kakeya sets in the affine plane AG(2; q) are point sets that are the union of lines, one through eve...
A set S in a group G is said to be small if there exist infinitely many pairwise disjoint translat...
Kakeya sets in the affine plane $\mathrm AG (2,q)$ are point sets that are the union of lines, one t...
The authors present a new example of a small Kakeya set in the affine plane AG(2,q) and they give th...
Abstract. For a finite vector space V and a non-negative integer r ≤ dimV we es-timate the smallest ...
In this paper we study the minimal number τ(S,G) of translates of an arbitrary subset S of a group G...
summary:The universality problem focuses on finding universal spaces in classes of topological space...
AbstractLet G be a finite group. Denote by r(G) the least cardinality of a subset A of G, satisfying...
The combinatorial notion of a "small set" in an abstract group was introduced by Bella and Malykhin....
We prove that the universal lattices -- the groups $G=\SL_d(R)$ where $R=\Z[x_1,...,x_k]$, have prop...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
Abstract. The word problem for discrete groups is well-known to be undecidable by a Turing Machine; ...
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Denote by d=d(G) and m=m(G), respectively, the smallest and the largest cardinality of a minimal gen...
It was proved by Banakh and Protasov that every group can be generated by a small set (in the sense ...
Kakeya sets in the affine plane AG(2; q) are point sets that are the union of lines, one through eve...
A set S in a group G is said to be small if there exist infinitely many pairwise disjoint translat...
Kakeya sets in the affine plane $\mathrm AG (2,q)$ are point sets that are the union of lines, one t...
The authors present a new example of a small Kakeya set in the affine plane AG(2,q) and they give th...
Abstract. For a finite vector space V and a non-negative integer r ≤ dimV we es-timate the smallest ...
In this paper we study the minimal number τ(S,G) of translates of an arbitrary subset S of a group G...
summary:The universality problem focuses on finding universal spaces in classes of topological space...
AbstractLet G be a finite group. Denote by r(G) the least cardinality of a subset A of G, satisfying...
The combinatorial notion of a "small set" in an abstract group was introduced by Bella and Malykhin....
We prove that the universal lattices -- the groups $G=\SL_d(R)$ where $R=\Z[x_1,...,x_k]$, have prop...
A Kakeya, or Besicovitch, set in a vector space is a set which contains a line in every direction. T...
Abstract. The word problem for discrete groups is well-known to be undecidable by a Turing Machine; ...
AbstractLet G be a group written multiplicatively. We say that G has the small sumsets property if f...
Denote by d=d(G) and m=m(G), respectively, the smallest and the largest cardinality of a minimal gen...