论文标题
所有有限套件都是最大规范的拉姆齐
All finite sets are Ramsey in the maximum norm
论文作者
论文摘要
对于两个度量空间$ \ MATHBB x $和$ \ MATHCAL y $，$ \ MATHBB x $的色度$χ（\ Mathbb x; \ Mathcal Y）$，with prebidden $ \ mathcal y $是最小的$ k $，是最小的$ \ Mathbb x $ $ \ k $ k $ y Mathc y yno $ k $ y y mons y和mons y monhonic y yonoch y y monhon y monhoins y mons y y monhoins在本文中，我们表明，对于每个有限的度量空间$ \ MATHCAL {m} $，其中至少包含两个点$χ\ weft（\ Mathbb r^n_ \ infty; \ Mathcal m \ right）$以$ n $的速度增长。我们还为某些特殊的$ \ Mathcal M $提供明确的下限和上限。
For two metric spaces $\mathbb X$ and $\mathcal Y$, the chromatic number $χ(\mathbb X;\mathcal Y)$ of $\mathbb X$ with forbidden $\mathcal Y$ is the smallest $k$ such that there is a coloring of the points of $\mathbb X$ with $k$ colors and no monochromatic copy of $\mathcal Y$. In this paper, we show that for each finite metric space $\mathcal{M}$ that contains at least two points the value $χ\left(\mathbb R^n_\infty; \mathcal M \right)$ grows exponentially with $n$. We also provide explicit lower and upper bounds for some special $\mathcal M$.
