论文标题
对角方程系统的分区规律性
Partition regularity for systems of diagonal equations
论文作者
论文摘要
我们考虑$ n $对角方程的系统。我们的主要结果表明，如果此类系统的系数矩阵足够非单位，则在满足RADO列的条件时，该系统是常规的分区。此外，如果该系统也接受恒定的解决方案，那么我们证明该系统在每一组正密度的整数上都具有非平凡的解决方案。
We consider systems of $n$ diagonal equations in $k$th powers. Our main result shows that if the coefficient matrix of such a system is sufficiently non-singular, then the system is partition regular if and only if it satisfies Rado's columns condition. Furthermore, if the system also admits constant solutions, then we prove that the system has non-trivial solutions over every set of integers of positive upper density.
