Abstract
In this article we explore an arithmetic analogue of a long-standing open problem
in graph theory: what can be said about the number of monochromatic additive configurations in 2-colourings of finite abelian groups? We are able to answer several instances of this question using techniques from additive combinatorics and quadratic Fourier analysis. However, the main purpose of this paper is to advertise this sphere of problems and to put forward a number of concrete questions and conjectures.
in graph theory: what can be said about the number of monochromatic additive configurations in 2-colourings of finite abelian groups? We are able to answer several instances of this question using techniques from additive combinatorics and quadratic Fourier analysis. However, the main purpose of this paper is to advertise this sphere of problems and to put forward a number of concrete questions and conjectures.
| Original language | English |
|---|---|
| Pages (from-to) | 125-140 |
| Number of pages | 16 |
| Journal | Quarterly Journal of Mathematics |
| Volume | 68 |
| Issue number | 1 |
| Early online date | 9 May 2016 |
| DOIs | |
| Publication status | Published - Mar 2017 |