Katalin Gyarmati

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For finite sets of integers A1, A2 . . . An we study the cardinality of the n-fold sumset A1 + · · ·+An compared to those of n−1-fold sumsets A1 + · · ·+Ai−1 + Ai+1 + . . . An. We prove a superadditivity and a submultiplicativity property for these quantities. We also examine the case when the addition of elements is restricted to an addition graph between(More)
The aim of this paper is to prove a general version of Plünnecke’s inequality. Namely, assume that for finite sets A, B1, . . . Bk we have information on the size of the sumsets A + Bi1 + · · · + Bil for all choices of indices i1, . . . il. Then we prove the existence of a non-empty subset X of A such that we have ‘good control’ over the size of the sumset(More)
Three constructions for binary lattices with strong pseudorandom properties are given. These constructions are the two dimensional extensions and modifications of three of the most important one dimensional constructions. The upper estimates for the pseudorandom measures of the binary lattices constructed are based on the principle that character sums in(More)
This paper concerns the study of the correlation measures of finite binary sequences, more particularily the dependence of correlation measures of even order and correlation measures of odd order. These results generalize previous results due to Gyarmati [7] and to Anantharam [3] and provide a partial answer to a conjecture due to Mauduit [12]. The last(More)