Gabriel Currier

collaborators

3 papers

math.CO2026

Improved bounds for lines and $1$ -separated sets in Euclidean Ramsey theory

Gabriel Currier, Param Mody, Zehan Xie +1

Let $K$ be a $1$ -separated set of diameter at most $R - 1$ , and let $ℓ_{m}$ denote a collection of $m$ points on a line, with consecutive points of distance $1$ apart. Conlon and Fo…

math.CO2024

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

Improved bounds for lines and 1-separated sets in Euclidean Ramsey theory

Avoiding short progressions in Euclidean Ramsey theory

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

Improved bounds for lines and $1$ -separated sets in Euclidean Ramsey theory