Kenneth Moore

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math.CO2026

A pyramid with a Ramsey base is Ramsey

Kenneth Moore

A finite subset $X$ of $R^{d}$ is called a Ramsey set if for any number of colours $k$ there exists a dimension $n$ such that whenever $R^{n}$ is $k$ -coloured there…

math.CO2026

On traces of randomly rolling polytopes

Kenneth Moore, János Pach

Let $P$ be a three-dimensional convex polytope resting with one of its faces on the plane. At each step, $P$ is allowed to roll over a randomly selected edge of…

math.CO2026

Point sets avoiding near-integer distances

Ritesh Goenka, Kenneth Moore

Let $d \in N$ , $I^´ \in (0, 1/2)$ , and $X > 0$ . Denote by $N_{d} (X, I^´)$ the maximum number of points in a subset of the closed Euclidean ball of radius $X$ in $R^{d}$ …

math.CO2026

Any 2-coloring of the plane contains monochromatic unit rhombuses

Kenneth Moore, Arsenii Sagdeev

In this note, we prove that any 2-coloring of the plane contains 4 points of the same color forming a rhombus with unit sides and non-unit diagonals, answering a question of Axenov…

math.CO2025

Avoiding short progressions in Euclidean Ramsey theory

Gabriel Currier, Kenneth Moore, Chi Hoi Yip

We provide a general framework to construct colorings avoiding short monochromatic arithmetic progressions in Euclidean Ramsey theory. Specifically, if $ℓ_{m}$ denotes $m$ colline…

math.CO2024

Any two-coloring of the plane contains monochromatic 3-term arithmetic progressions

Gabriel Currier, Kenneth Moore, Chi Hoi Yip

A conjecture of ErdÅs, Graham, Montgomery, Rothschild, Spencer and Straus states that, with the exception of equilateral triangles, any two-coloring of the plane will have a monoc…