EuDML | Browse

Let $G$ be an abelian group and $A, B$ two subsets of equal size $k$ such that $A + B$ and $A + A$ both have size $2 k - 1$ . Answering a question of Bihani and Jin, we prove that if $A + B$ is aperiodic or if there exist elements $a \in A$ and $b \in B$ such that $a + b$ has a unique expression as an element of $A + B$ and $a + a$ has a unique expression as an element of $A + A$ , then $A$ is a translate of $B$ . We also give an explicit description of the various counterexamples which arise when neither condition holds.

Solving a linear equation in a set of integers I

Imre Z. Ruzsa (1993)

Acta Arithmetica

Solving a linear equation in a set of integers II

Imre Z. Ruzsa (1995)

Acta Arithmetica

Some additive and multiplicative problem sin number theory

S. Choi, P. Erdös, E. Szemerédi (1975)

Acta Arithmetica

Some additive applications of the isoperimetric approach

Yahya O. Hamidoune (2008)

Annales de l’institut Fourier

Let $G$ be a group and let $X$ be a finite subset. The isoperimetric method investigates the objective function $| (X B) ∖ X |$ , defined on the subsets $X$ with $| X | \geq k$ and $| G ∖ (X B) | \geq k$ , where $X B$ is the product of $X$ by $B$ .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.

Janjić, Milan (2009)

Journal of Integer Sequences [electronic only]

Some explicit constructions of sets with more sums than differences

Peter V. Hegarty (2007)

Acta Arithmetica

Some problems of combinatorial number theory related to Bertrand's postulate.

Greenfield, Lawrence E., Greenfield, Stephen J. (1998)

Journal of Integer Sequences [electronic only]

Some properties of the multiple binomial transform and the Hankel transform of shifted sequences.

Pan, Jiaqiang (2011)

Journal of Integer Sequences [electronic only]

Some results in additive number theory I: The critical pair theory

Yahya Ould Hamidoune (2000)

Acta Arithmetica

Some solved and unsolved problems in combinatorial number theory, ii

P. Erdős, A. Sárközy (1993)

Colloquium Mathematicae

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.

Currently displaying 1 – 20 of 36

Page 1 Next