# All finite sets are Ramsey in the maximum norm

@article{Kupavskii2021AllFS, title={All finite sets are Ramsey in the maximum norm}, author={Andrey B. Kupavskii and A. A. Sagdeev}, journal={Forum of Mathematics, Sigma}, year={2021}, volume={9} }

Abstract For two metric spaces $\mathbb X$ and $\mathcal Y$ the chromatic number $\chi ({{\mathbb X}};{{\mathcal{Y}}})$ of $\mathbb X$ with forbidden $\mathcal Y$ is the smallest k such that there is a colouring of the points of $\mathbb X$ with k colors that contains no monochromatic copy of $\mathcal Y$. In this article, we show that for each finite metric space $\mathcal {M}$ that contains at least two points the value $\chi \left ({{\mathbb R}}^n_\infty; \mathcal M \right )$ grows…

## 6 Citations

Max-norm Ramsey Theory

- Mathematics
- 2021

Given a metric space M that contains at least two points, the chromatic number χ (Rn∞,M) is defined as the minimum number of colours needed to colour all points of an n−dimensional space Rn∞ with the…

Two-colorings of the normed spaces without long monochromatic unit arithmetic progressions

- Mathematics
- 2022

Given a natural n, we construct a two-coloring of an n-dimensional space with the maximum metric satisfying the following. For any finite set of reals S with diameter greater than 5 such that the…

On Ramsey Numbers for Arbitrary Sequences of Graphs

- MathematicsDoklady Mathematics
- 2022

Abstract In this work, we study nontrivial generalizations of Ramsey numbers to the case of arbitrary sequences of graphs. For many classes of sequences, exact values or asymptotics of Ramsey numbers…

Solution to a conjecture of Schmidt and Tuller on linear packings and coverings

- Mathematics
- 2022

In 2008, Schmidt and Tuller stated a conjecture concerning optimal packing and covering of integers by translates of a given three-point set. In this note, we confirm their conjecture and relate it…

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