113 citations · 133 across the 9 of their papers we have counts for
5 papers · 1 filter
A Szemeredi-type regularity lemma in abelian groups, with applications
Ben Green
Szemeredi's regularity lemma is an important tool in graph theory which has applications throughout combinatorics. In this paper we prove an analogue of Szemeredi's regularity lemm…
Sum-free sets in abelian groups
Ben Green, Imre Z. Ruzsa
Let A be a subset of an abelian group G. We say that A is sum-free if there do not exist x,y and z in A satisfying x + y = z. We determine, for any G, the cardinality of the larges…
The Cameron-Erdos Conjecture
Ben Green
A set A of integers is said to be sum-free if there are no solutions to the equation x + y = z with x,y and z all in A. Answering a question of Cameron and Erdos, we show that the…
Counting sets with small sumset, and the clique number of random Cayley graphs
Ben Green
Given a set A in Z/NZ we may form a Cayley sum graph G_A on vertex set Z/NZ by joining i to j if and only if i + j is in A. We investigate the extent to which performing this const…
Roth's theorem in the primes
Ben Green
We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called…