Degree of Regularity of Linear Homogeneous Equations
Combinatorics
2014-11-12 v3
Abstract
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.
Keywords
Cite
@article{arxiv.1309.7220,
title = {Degree of Regularity of Linear Homogeneous Equations},
author = {Kavish Gandhi and Noah Golowich and László Miklós Lovász},
journal= {arXiv preprint arXiv:1309.7220},
year = {2014}
}
Comments
7 pages. This is an update of our previous version that proves a stronger result