Partition regularity of a system of De and Hindman

TL;DR

This paper demonstrates that a specific matrix, not partition regular over real numbers near zero, is partition regular over natural numbers, resolving a question posed by De and Hindman.

Contribution

It establishes the partition regularity of a matrix over natural numbers despite its non-regularity over reals near zero, answering an open question.

Findings

Matrix is not image partition regular over R near zero.

Matrix is image partition regular over N.

Addresses a question of De and Hindman.

Abstract

We prove that a certain matrix, which is not image partition regular over R near zero, is image partition regular over N. This answers a question of De and Hindman.