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

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…