Solving a linear equation in a set of integers I
Solving a linear equation in a set of integers II
Some additive and multiplicative problem sin number theory
Some additive applications of the isoperimetric approach
Let be a group and let be a finite subset. The isoperimetric method investigates the objective function , defined on the subsets with and , where is the product of by .In this paper we present all the basic facts about the isoperimetric method. We improve some of our previous results and obtain generalizations and short proofs for several known results. We also give some new applications.Some of the results obtained here will be used in coming papers to improve Kempermann structure...
Some classes of numbers and derivatives.
Some explicit constructions of sets with more sums than differences
Some problems of combinatorial number theory related to Bertrand's postulate.
Some properties of the multiple binomial transform and the Hankel transform of shifted sequences.
Some results in additive number theory I: The critical pair theory
Some solved and unsolved problems in combinatorial number theory, ii
In an earlier paper [9], the authors discussed some solved and unsolved problems in combinatorial number theory. First we will give an update of some of these problems. In the remaining part of this paper we will discuss some further problems of the two authors.
Some sufficient conditions for zero asymptotic density and the expression of natural numbers as sum of values of special functions
This paper generalizes some results from another one, namely [3]. We have studied the issues of expressing natural numbers as a sum of powers of natural numbers in paper [3]. It means we have studied sets of type where were given natural numbers. Now we are going to study a more general case, i.e. sets of natural numbers that are expressed as sum of integral parts of functional values of some special functions. It means that we are interested in sets of natural numbers in the form
Some values of Olson's constant.
Stapled sequences and stapling coverings of natural numbers.
Stern polynomials and double-limit continued fractions
Subset sums avoiding quadratic nonresidues
Subset sums modulo a prime
Subsums of a zero-sum free subset of an abelian group.
Sum-dominant sets and restricted-sum-dominant sets in finite abelian groups
We call a subset A of an abelian group G sum-dominant when |A+A| > |A-A|. If |A⨣A| > |A-A|, where A⨣A comprises the sums of distinct elements of A, we say A is restricted-sum-dominant. In this paper we classify the finite abelian groups according to whether or not they contain sum-dominant sets (respectively restricted-sum-dominant sets). We also consider how much larger the sumset can be than the difference set in this context. Finally, generalising work of Zhao, we provide asymptotic estimates...
Sums of distinct residues mod p
Sums of like powers and some dense sets.