Analogues of van der Waerden’s theorem on arithmetic progressions are considered where the family of all arithmetic progressions, AP, is replaced by some subfamily of AP. Specifically, we want to know for which sets A, of positive integers, the following statement holds: for all positive integers r and k, there exists a positive integer n = w0(k;r) such that for every r-coloring for of [1;n] there exists a monochromatic k-term arithmetic progression whose common difference belongs to A. We will call any subset of the positive integers that has the above property large. A set having this property for a specific fixed r will be called r-large. We give some necessary conditions for a set to be large, including the fact that every large set mus...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
A classic theorem of van der Waerden asserts that for any positive integer k, there is an integer W(...
Abstract. This is a short exposition of the dynamical approach to the proof of van der Waerden’s the...
Abstract. Analogues of van der Waerden’s theorem on arithmetic progressions are considered where the...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
AbstractA classic theorem of van der Waerden asserts that for any positive integer k, there is an in...
AbstractFor positive integers n and k, let rk(n) be the size of the largest subset of {1,2,…,n} with...
AbstractVan der Waerden's classical theorem on arithmetic progressions states that for any positive ...
abstract: Van der Waerden’s Theorem asserts that for any two positive integers k and r, one may find...
AbstractA 2-coloring of the non-negative integers and a function h are given such that if P is any m...
Recall that van der Waerden's theorem states that any finite coloring of the naturals has arbitraril...
AbstractF. Cohen raised the following question: Determine or estimate a function F(d) so that if we ...
Consider a coloring of {1, 2,... ,n} in 3 colors, where n ≡ 0 (mod 3). If all the color classes have...
AbstractFor each positive integer n, G(n) is defined to be the largest integer k such that no matter...
We study the length of monochromatic arithmetic progressions in the Thue–Morse word and in a class o...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
A classic theorem of van der Waerden asserts that for any positive integer k, there is an integer W(...
Abstract. This is a short exposition of the dynamical approach to the proof of van der Waerden’s the...
Abstract. Analogues of van der Waerden’s theorem on arithmetic progressions are considered where the...
An arithmetic progression is a sequence of numbers such that the difference between the consecutive ...
AbstractA classic theorem of van der Waerden asserts that for any positive integer k, there is an in...
AbstractFor positive integers n and k, let rk(n) be the size of the largest subset of {1,2,…,n} with...
AbstractVan der Waerden's classical theorem on arithmetic progressions states that for any positive ...
abstract: Van der Waerden’s Theorem asserts that for any two positive integers k and r, one may find...
AbstractA 2-coloring of the non-negative integers and a function h are given such that if P is any m...
Recall that van der Waerden's theorem states that any finite coloring of the naturals has arbitraril...
AbstractF. Cohen raised the following question: Determine or estimate a function F(d) so that if we ...
Consider a coloring of {1, 2,... ,n} in 3 colors, where n ≡ 0 (mod 3). If all the color classes have...
AbstractFor each positive integer n, G(n) is defined to be the largest integer k such that no matter...
We study the length of monochromatic arithmetic progressions in the Thue–Morse word and in a class o...
integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily lo...
A classic theorem of van der Waerden asserts that for any positive integer k, there is an integer W(...
Abstract. This is a short exposition of the dynamical approach to the proof of van der Waerden’s the...