We present general sufficient and necessary conditions for the partition regularity of
Diophantine equations, which extend the classic Rado's Theorem by covering large classes …

We show that for every finite colouring of the natural numbers there exists $ a, b> 1$ such
that the triple $\{a, b, a^ b\} $ is monochromatic. We go on to show the partition regularity of a …

Fermat-like equations that are not partition regular Page 1 COMBINATORICA Bolyai Society
– Springer-Verlag 0209–9683/118/$6.00 c 2018 János Bolyai Mathematical Society and …

Abstract Let n∈ N, R be a binary relation on [n], and C 1 (i, j),…, C n (i, j)∈ Z, for i, j∈[n]. We
define the exponential system of equations E (R,(C k (i, j) i, j, k) to be the system X i Y 1 C 1 …

SURVEY A history of central sets Page 1 Ergod. Th. & Dynam. Sys. (2020), 40, 1–33 doi:10.1017/etds.2018.37
c Cambridge University Press, 2018 SURVEY A history of central sets NEIL HINDMAN …

We show how multiplicatively syndetic sets can be used in the study of partition regularity of
dilation invariant systems of polynomial equations. In particular, we prove that a dilation …

A finite or infinite matrix $ A $ with rational entries (and only finitely many non-zero entries in
each row) is called image partition regular if, whenever the natural numbers are finitely …

We introduce two natural notions of cogrowth for finitely generated semigroups—one local
and one global—and study their relationship with amenability and random walks. We …

A system of linear equations with integer coefficients is partition regular over a subset S of
the reals if, whenever S∖{0} is finitely coloured, there is a solution to the system contained in …

Recent results on partition regularity of infinite matrices Page 215 12 Recent Results on
Partition Regularity of Infinite Matrices Neil Hindman Abstract We survey results obtained in …