%0 Journal Article
%T Degree of Regularity of Linear Homogeneous Equations
%A Kavish Gandhi
%A Noah Golowich
%A L¨˘szl¨® Mikl¨®s Lov¨˘sz
%J Mathematics
%D 2013
%I arXiv
%R 10.4310/JOC.2014.v5.n2.a5
%X We define a linear homogeneous equation to be strongly r-regular if, when a finite number of inequalities is added to the equation, the system of the equation and inequalities is still r-regular. In this paper, we show that, if a linear homogeneous equation is r-regular, then it is strongly r-regular. In 2009, Alexeev and Tsimerman introduced a family of equations, each of which is (n-1)-regular but not n-regular, verifying a conjecture of Rado from 1933. These equations are actually strongly (n-1)-regular as an immediate corollary of our results.
%U http://arxiv.org/abs/1309.7220v3