AI 中文总结
本文针对欧氏拉姆齐理论中Ivan等人提出的问题，证明了在拉姆齐集的仿射包外添加点得到的棱锥仍为拉姆齐集，解决了拉姆齐集分类的相关问题。
AI 中文摘要
若对于任意颜色数k，均存在维度n，使得当ℝⁿ被k染色时，总能找到一个单色的与X全等的副本，则称ℝᵈ的有限子集X为拉姆齐集。拉姆齐集的分类是欧氏拉姆齐理论领域的主要未解决问题之一。为此，Ivan、Leader和Walters近期提出问题：在拉姆齐集的仿射包外添加一个点，是否必然得到另一个拉姆齐集。本文中，我们对该问题给出了肯定回答。
英文摘要
A finite subset $X$ of ${\mathbb R}^d$ is called a Ramsey set if for any number of colours $k$ there exists a dimension $n$ such that whenever ${\mathbb R}^n$ is $k$-coloured there exists a monochromatic congruent copy of $X$. The classification of Ramsey sets is one of the major unsolved problems in the field of Euclidean Ramsey theory. Towards this, Ivan, Leader and Walters recently asked whether adding a point to a Ramsey set outside of its affine hull necessarily produces another Ramsey set. In this note, we answer their question in the affirmative.
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