12 citations · 28 across the 5 of their papers we have counts for
4 papers · 1 filter
On sumsets of dissociated sets
I. D. Shkredov
In the paper we are studying some properties of subsets Q of sums of dissociated sets. The exact upper bound for the number of solutions of the following equation (1) q_1 + ... + q…
On a two-dimensional analog of Szemeredi's Theorem in Abelian groups
I. D. Shkredov
Let G be a finite Abelian group and A be a subset G\times G of cardinality at least |G|^2/(log log |G|)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,…
On sets with small doubling
I. D. Shkredov
Let G be an arbitrary Abelian group and let A be a finite subset of G. A has small additive doubling if |A+A| < K|A| for some K>0. These sets were studied in papers of G.A. Freiman…
On a Generalization of Szemeredi's Theorem
I. D. Shkredov
Let A \subseteq [1,..,N]^2 be a set of cardinality at least N^2/(log log N)^c, where c>0 is an absolute constant. We prove that A contains a triple {(k,m), (k+d,m), (k,m+d)}, where…