5 citations · 21 across the 28 of their papers we have counts for
17 papers · 1 filter
The spanning number and the independence number of a subset of an abelian group
Bela Bajnok
Let be a subset of a finite abelian group . We call {\it -independent} in , if whenever for some integer…
On sumsets of nonbases of maximum size
Bela Bajnok, Peter Pal Pach
Let be a finite abelian group. A nonempty subset in is called a basis of order if ; when , it is called a nonbasis of order . Our interest is in…
On Perfect Bases in Finite Abelian Groups
Bela Bajnok, Connor Berson, Hoang Anh Just
Let be a finite abelian group and be a positive integer. A subset of is called a {\em perfect -basis of } if each element of can be written uniquely as th…
A Walk Through Some Newer Parts of Additive Combinatorics
Bela Bajnok
In this survey paper we discuss some recent results and related open questions in additive combinatorics, in particular, questions about sumsets in finite abelian groups.
Additive Combinatorics in Groups and Geometric Combinatorics on Spheres
Bela Bajnok
We embark on a tour that takes us through four closely related topics: the dual concepts of independence and spanning in finite abelian groups and the analogous dual concepts of de…
The Maximum Size of -Sum-Free Sets in Cyclic Groups
Béla Bajnok, Ryan Matzke
A subset of a finite abelian group is called -sum-free if the sum of (not-necessarily-distinct) elements of never equals the sum of (not-necessarily-dist…
Additive Combinatorics: A Menu of Research Problems
Bela Bajnok
This text contains over three hundred specific open questions on various topics in additive combinatorics, each placed in context by reviewing all relevant results. While the prima…
More on the -critical numbers of finite abelian groups
Bela Bajnok
For a finite abelian group , a nonempty subset of , and a positive integer , we let denote the -fold sumset of ; that is, is the collection of sums of…
On two questions about restricted sumsets in finite abelian groups
Béla Bajnok, Samuel Edwards
Let be an abelian group of finite order , and let be a positive integer. A subset of is called {\em weakly -incomplete}, if not every element of can be wr…
On Asymptotic Approximate Groups of Integers
Bela Bajnok
Let be a positive integer, and let be a nonempty finite set of at least two integers. We let denote the {\em asymptotic -covering number} of , that i…
Comments on Y. O. Hamidoune's Paper "Adding Distinct Congruence Classes"
Béla Bajnok
The main result in Y.~O.~Hamidoune's paper "Adding Distinct Congruence Classes" ({\em Combin.~Probab.~Comput.}~{\bf 7} (1998) 81-87) is as follows: If is a generating subset of…
A Constructive Finite Field Method for Scattering Points on the Surface of -Dimensional Spheres
Béla Bajnok, Steven B. Damelin, Jenny Li +1
In this exploratory article, we present a constructive method for scattering points on the surface of dimensional spheres which we believe is new and of interest. Indeed, the p…
Open problems about sumsets in finite abelian groups: minimum sizes and critical numbers
Béla Bajnok
For a positive integer and a subset of a given finite abelian group, we let , , and denote the -fold sumset, restricted sumset, and signed s…
The -critical number of finite abelian groups
Bela Bajnok
For a finite abelian group and a positive integer , the unrestricted (resp.~restricted) -critical number (resp.~) of is defined to be the min…
On the Minimum Size of Signed Sumsets in Elementary Abelian Groups
Bela Bajnok, Ryan Matzke
For a finite abelian group and positive integers and , we let and $$ρ_{\pm} (G, m, h) = \min \{|h_{\pm} A| \;…
The Minimum Size of Signed Sumsets
Bela Bajnok, Ryan Matzke
For a finite abelian group and positive integers and , we let and $$ρ_{\pm} (G, m, h) = \min \{|h_{\pm} A| \;…
On the minimum size of restricted sumsets in cyclic groups
Béla Bajnok
For positive integers , , and , we let denote the minimum size of the -fold restricted sumset among all -subsets of the cyclic group…