关于无线性方程单色解的极小着色
组合数学
2010-09-23 v1
摘要
对于环R和线性齐次方程组L，如果R的非零元素的一个着色不存在L的单色解，并且该着色使用了尽可能少的颜色，则称该着色对L是极小的。对于有理数q和正整数n，令E(q,n)表示方程。我们对q属于{3/2,2,3,4}的每个方程E(q,3)、n属于{3,4,5,6}的E(2,n)以及x_1+x_2+x_3=4x_4，分类了非零有理数的极小着色。这些结果引出了几个关于极小着色的开放问题与猜想。
引用
@article{arxiv.1009.4234,
title = {On minimal colorings without monochromatic solutions to a linear equation},
author = {Boris Alexeev and Jacob Fox and Ron Graham},
journal= {arXiv preprint arXiv:1009.4234},
year = {2010}
}
备注
14 pages, 1 very complicated table. This article originally appeared in the journal INTEGERS in 2007. This version differs from that journal version only in formatting. As such, note that the author contact info is outdated and at least one conjecture contained within has been resolved