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Dive into the research topics where Neil Hindman is active.

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Featured researches published by Neil Hindman.


Journal of Combinatorial Theory | 1974

Finite sums from sequences within cells of a partition of N

Neil Hindman

Abstract The principal result of this paper establishes the validity of a conjecture by Graham and Rothschild. This states that, if the natural numbers are divided into two classes, then there is a sequence drawn from one of those classes such that all finite sums of distinct members of that sequence remain in the same class.


Transactions of the American Mathematical Society | 1979

Partitions and sums and products of integers

Neil Hindman

The principal result of the paper is that, if r < u and (A¡)i<r is a partition of u, then there exist i < r and infinite subsets B and C of to such that 2 F e A¡ and IIG G A¡ whenever F and G are finite nonempty subsets of B and C respectively. Conditions on the partition are obtained which are sufficient to guarantee that B and C can be chosen equal in the above statement, and some related finite questions are investigated.


Combinatorics, Probability & Computing | 2003

Open Problems in Partition Regularity

Neil Hindman; Imre Leader; Dona Strauss

A finite or infinite matrix


Journal of Combinatorial Theory | 2006

Multiplicative structures in additively large sets

Mathias Beiglböck; Vitaly Bergelson; Neil Hindman; Dona Strauss

A


Transactions of the American Mathematical Society | 2003

Infinite partition regular matrices: solutions in central sets

Neil Hindman; Imre Leader; Dona Strauss

with rational entries is called partition regular if, whenever the natural numbers are finitely coloured, there is a monochromatic vector


Journal of Combinatorial Theory | 2001

Partition Regular Structures Contained in Large Sets Are Abundant

Vitaly Bergelson; Neil Hindman

x


Transactions of the American Mathematical Society | 1987

On strongly summable ultrafilters and union ultrafilters

Andreas Blass; Neil Hindman

with


Combinatorica | 1995

Infinite partition regular matrices

Walter A. Deuber; Neil Hindman; Imre Leader; Hanno Lefmann

Ax=0


Combinatorica | 1994

On IP* sets and central sets

Vitaly Bergelson; Neil Hindman

. Many of the classical theorems of Ramsey Theory may naturally be interpreted as assertions that particular matrices are partition regular.While in the finite case partition regularity is well understood, very little is known in the infinite case. Our aim in this paper is to present some of the natural and appealing open problems in the area.


Transactions of the American Mathematical Society | 1984

Filters and the weak almost periodic compactification of a discrete semigroup

John F. Berglund; Neil Hindman

Previous research extending over a few decades has established that multiplicatively large sets (in any of several interpretations) must have substantial additive structure. We investigate here the question of how much multiplicative structure can be found in additively large sets. For example, we show that any translate of a set of finite sums from an infinite sequence must contain all of the initial products from another infinite sequence. And, as a corollary of a result of Renling Jin, we show that if A and B have positive upper Banach density, then A + B contains all of the initial products from an infinite sequence. We also show that if a set has a complement which is not additively piecewise syndetic, then any translate of that set is both additively and multiplicatively large in several senses.We investigate whether a subset of N with bounded gaps--a syndetic set--must contain arbitrarily long geometric progressions. We believe that we establish that this is a significant open question.

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Imre Leader

University of Cambridge

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Ben Barber

University of Birmingham

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