AbstractWe obtain upper and lower bounds for the size of a largest family of 3-term arithmetic progressions contained in [0,n-1], no two of which intersect in more than one point. Such a family consists of just under a half of all of the 3-term arithmetic progressions contained in [0,n-1]
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
Given a density 0 < σ ≤ 1, we show for all sufficiently large primes p that if S ⊆ Z/pZ has the l...
We obtain upper and lower bounds for the size of a largest family of 3-term arithmetic progressions ...
Varnavides proved, as a result of Roth’s theorem, a lower bound on the number of three term arithmet...
Title: Roth's theorem on arithmetic progressions Author: Michal Krkavec Department: Department of Ap...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Abstract. Let T be a collection of 3-element subsets S of {1,..., n} with the property that if i <...
AbstractFor given n, k, the minimum cardinal of any subset B of [1, n] which meets all of the k-term...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showi...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
AbstractThere has been much work on the following question: given n, how large can a subset of {1,…,...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
Given a density 0 < σ ≤ 1, we show for all sufficiently large primes p that if S ⊆ Z/pZ has the l...
We obtain upper and lower bounds for the size of a largest family of 3-term arithmetic progressions ...
Varnavides proved, as a result of Roth’s theorem, a lower bound on the number of three term arithmet...
Title: Roth's theorem on arithmetic progressions Author: Michal Krkavec Department: Department of Ap...
AbstractWe give a complete characterization of so-called powerful arithmetic progressions, i.e. of p...
Abstract. Let T be a collection of 3-element subsets S of {1,..., n} with the property that if i <...
AbstractFor given n, k, the minimum cardinal of any subset B of [1, n] which meets all of the k-term...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
Let B be a set of natural numbers of size n. We prove that the length of the longest arithmetic prog...
We improve the quantitative estimate for Roth's theorem on three-term arithmetic progressions, showi...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
AbstractThere has been much work on the following question: given n, how large can a subset of {1,…,...
AbstractGiven a density 0<σ⩽1, we show for all sufficiently large primes p that if S⊆Z/pZ has the le...
Let B be a set of real numbers of size n. We prove that the length of the longest arithmetic progres...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
Given a density 0 < σ ≤ 1, we show for all sufficiently large primes p that if S ⊆ Z/pZ has the l...
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