Let A and B be randomly chosen s-subsets of the first n integers such that their sumset A+B has size at most Ks. We show that asymptotically almost surely A and B are almost fully contained in arithmetic progressions PA ...

Presentem algunes tècniques elementals de l’anàlisi de Fourier dins la combinatòria aritmètica i les usem per demostrar resultats de caràcter combinatori a conjunts de Sidon grans. Per una banda, demostrem que els conjunts ...

The Lonely Runner Conjecture, posed independently by Wills and by Cusick, states that for any set of runners running along the unit circle with constant different speeds and starting at the same point, there is a time where ...

In this thesis we present several analogies betweeen sumset inequalities and entropy inequalities. We offer an overview of the different results and techniques that have been developed during the last ten years, starting ...

Farey sequences of irreducible fractions between 0 and 1 can be related to graph constructions known as Farey graphs. These graphs were first introduced by Matula and Kornerup in 1979 and further studied by Colbourn in ...

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We prove that, for all q=2 and for all invertible residue classes a modulo q, there exists a natural number n=(650q)9 that is congruent to a modulo q and that is the product of exactly three primes, all of which are below ...

We give explicit formulae for obtaining the binary sequences which produce Steinhaus triangles and generalized Pascal triangles with rotational and dihedral symmetries.

The need of solving linear systems with circulant matrices occursin many problems related to the periodicity of that problem. This class ofsystem appears in many applications that range from numerical solution ofpartial ...