TY - JOUR
T1 - Ramsey multiplicity of linear patterns in certain finite abelian groups
AU - Saad, Alex
AU - Wolf, Julia
PY - 2017/3
Y1 - 2017/3
N2 - In this article we explore an arithmetic analogue of a long-standing open problemin 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.
AB - In this article we explore an arithmetic analogue of a long-standing open problemin 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.
U2 - 10.1093/qmath/haw011
DO - 10.1093/qmath/haw011
M3 - Article
VL - 68
SP - 125
EP - 140
JO - Quarterly Journal of Mathematics
JF - Quarterly Journal of Mathematics
SN - 0033-5606
IS - 1
ER -