论文标题
Ramsey功能方程理论的限制结果
A limiting result for the Ramsey theory of functional equations
论文作者
论文摘要
我们研究了功能方程的系统，其解决方案可以通过一个变量的函数进行参数化；我们的主要结果证明，这种系统的分区规律性（PR）可以完全以恒定解决方案的存在为特征。作为此结果的应用，我们证明了以下内容：（1）在$ \ mathbb {n} $上方，在两个变量中对二磷剂方程系统的PR进行完整表征。特别是，我们证明了两个变量中唯一的无限不可约的方程是$ x = y $; （2）$ s $单位方程的PR和Rado定理的故障，用于有限生成的$ \ Mathbb {C} $的乘法子组； （3）两类多项式指数方程的PR的完整表征。
We study systems of functional equations whose solutions can be parameterized in function of one variable; our main result proves that the partition regularity (PR) of such systems can be completely characterized by the existence of constant solutions. As applications of this result, we prove the following: (1) A complete characterization of the PR of systems of Diophantine equations in two variables over $\mathbb{N}$. In particular, we prove that the only infinitely PR irreducible equation in two variables is $x=y$; (2) PR of $S$-unit equations and the failure of Rado's Theorem for finitely generated multiplicative subgroups of $\mathbb{C}$; and (3) a complete characterization of the PR of two classes of polynomial exponential equations.
