AbstractFor a sequence of rectangles R=(Rk)k=1∞ in Nd and a subset F of Nd, when the limit exists set d(F,R)=limk→∞|F∩Rk||Rk|. Suppose the subset E of Nd has positive Banach density B(E). We give conditions on R to ensure there exists a subset S of Nd with d(S,R)≥B(E) such that for each finite subset {m1,…,mr} of S we have B(E∩(E+m1)∩⋯∩(E+mr))>0
Ahlswede R, Khachatrian LH. Density inequalities for sets of multiples. JOURNAL OF NUMBER THEORY. 19...
Abstract. Let N be a set of positive integers and let F(z) = I Anz" be an entire function for ...
AbstractWe will prove that if A, B are subsets of the real line R with positive outer Lebesgue measu...
AbstractLet A denote a strictly increasing sequence of integers; for any integer n, define A(n) to b...
International audienceLet $\mathrm{d}(A)$ be the asymptotic density (if it exists) of a sequence of ...
AbstractIn this note we prove that for every sequence (mq)q of positive integers and for every real ...
Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach densi...
Plünnecke proved that if B ⊆ N is a basis of order h> 1, i.e., σ(hB) = 1, then σ(A+B)> σ(A)1 ...
36 pagesInternational audienceDeveloping an idea of M. Gromov, we study the intersection formula for...
In 1977 L.T. Ramsey showed that any sequence in Z 2 with bounded gaps contains arbitrarily many coll...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
AbstractIn this note we give a combinatorial characterization of the set of density points for a cla...
We give several sufficient conditions on an infinite integer matrix (dij) for the set R = {Σij∈α, i\...
AbstractGiven a set A whose density and Banach density are equal (such sets can be found “inside” an...
AbstractThe aim of this paper is to study the maximal density attainable by a sequence S of positive...
Ahlswede R, Khachatrian LH. Density inequalities for sets of multiples. JOURNAL OF NUMBER THEORY. 19...
Abstract. Let N be a set of positive integers and let F(z) = I Anz" be an entire function for ...
AbstractWe will prove that if A, B are subsets of the real line R with positive outer Lebesgue measu...
AbstractLet A denote a strictly increasing sequence of integers; for any integer n, define A(n) to b...
International audienceLet $\mathrm{d}(A)$ be the asymptotic density (if it exists) of a sequence of ...
AbstractIn this note we prove that for every sequence (mq)q of positive integers and for every real ...
Renling Jin proved that if A and B are two subsets of the natural numbers with positive Banach densi...
Plünnecke proved that if B ⊆ N is a basis of order h> 1, i.e., σ(hB) = 1, then σ(A+B)> σ(A)1 ...
36 pagesInternational audienceDeveloping an idea of M. Gromov, we study the intersection formula for...
In 1977 L.T. Ramsey showed that any sequence in Z 2 with bounded gaps contains arbitrarily many coll...
AbstractErdős and Sárkőzy proposed the problem of determining the maximal density attainable by a se...
AbstractIn this note we give a combinatorial characterization of the set of density points for a cla...
We give several sufficient conditions on an infinite integer matrix (dij) for the set R = {Σij∈α, i\...
AbstractGiven a set A whose density and Banach density are equal (such sets can be found “inside” an...
AbstractThe aim of this paper is to study the maximal density attainable by a sequence S of positive...
Ahlswede R, Khachatrian LH. Density inequalities for sets of multiples. JOURNAL OF NUMBER THEORY. 19...
Abstract. Let N be a set of positive integers and let F(z) = I Anz" be an entire function for ...
AbstractWe will prove that if A, B are subsets of the real line R with positive outer Lebesgue measu...
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