Fix α ∈ (0, 1/3). We show that, from a topological point of view, almost all sets A ⊆ N have the property that, if A 0 = A for all but o(n α ) elements, then A 0 is not a nontrivial sumset B + C. In particular, almost all A are totally irreducible. In addition, we prove that the measure analogue holds with α = 1
AbstractSuppose ε > 0 and k > 1. We show that if n > n0(k, ε) and A ⊆ Zn satisfies |A| > ((1k) + ε)n...
Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whethe...
Let S be a discrete semigroup and let the Stone–Čech compactification βS of S have the operation ext...
Fix α ∈ (0, 1/3). We show that, from a topological point of view, almost all sets A ⊆ N have the pro...
Fix $\alpha \in (0,1/3)$. We show that, from a topological point of view, almost all sets $A\subsete...
AbstractIf the positive integers are partitioned into a finite number of cells, then Hindman proved ...
Arithmetic quasidensities are a large family of real-valued set functions partially defined on the p...
AbstractLet {a1,a2,a3,…} be an unbounded sequence of positive integers with an+1/an approaching α as...
Erdős conjectured that for any set A of natural numbers with positive lower asymptotic density, ther...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
Beiglboeck, Bergelson and Fish proved that if subsets A,B of a countable discrete amenable group G h...
We say that I is an irredundant family if no element of I is a subset mod finite of a union of finit...
AbstractLet a be an infinite cardinal, let k be a cardinal with k < α, and denote by P(α) the power ...
In relation to the Erd\H os similarity problem (show that for any infinite set $A$ of real numbers t...
In this note we will show that for every natural number n \u3e 0 there exists an S ⊂ [0, 1] such tha...
AbstractSuppose ε > 0 and k > 1. We show that if n > n0(k, ε) and A ⊆ Zn satisfies |A| > ((1k) + ε)n...
Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whethe...
Let S be a discrete semigroup and let the Stone–Čech compactification βS of S have the operation ext...
Fix α ∈ (0, 1/3). We show that, from a topological point of view, almost all sets A ⊆ N have the pro...
Fix $\alpha \in (0,1/3)$. We show that, from a topological point of view, almost all sets $A\subsete...
AbstractIf the positive integers are partitioned into a finite number of cells, then Hindman proved ...
Arithmetic quasidensities are a large family of real-valued set functions partially defined on the p...
AbstractLet {a1,a2,a3,…} be an unbounded sequence of positive integers with an+1/an approaching α as...
Erdős conjectured that for any set A of natural numbers with positive lower asymptotic density, ther...
AbstractA finite set of distinct integers is called an r-set if it contains at least r elements not ...
Beiglboeck, Bergelson and Fish proved that if subsets A,B of a countable discrete amenable group G h...
We say that I is an irredundant family if no element of I is a subset mod finite of a union of finit...
AbstractLet a be an infinite cardinal, let k be a cardinal with k < α, and denote by P(α) the power ...
In relation to the Erd\H os similarity problem (show that for any infinite set $A$ of real numbers t...
In this note we will show that for every natural number n \u3e 0 there exists an S ⊂ [0, 1] such tha...
AbstractSuppose ε > 0 and k > 1. We show that if n > n0(k, ε) and A ⊆ Zn satisfies |A| > ((1k) + ε)n...
Given $A$ a set of $N$ positive integers, an old question in additive combinatorics asks that whethe...
Let S be a discrete semigroup and let the Stone–Čech compactification βS of S have the operation ext...
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