Jacob Fox

collaborators

2 papers

math.CO2026

A new lower bound for two-color van der Waerden numbers

Marcelo Campos, Jacob Fox, Carl Schildkraut

The van der Waerden number $w (k)$ is the smallest positive integer $N$ such that every two-coloring of ${1, 2, \dots, N}$ contains a monochromatic $k$ -term arithmetic progression.…

math.CO2026

On nearly consecutive sequences without long arithmetic progressions

Jacob Fox, Carl Schildkraut

A sequence $a_{1}, \dots, a_{n}$ of integers is nearly consecutive if $a_{i + 1} - a_{i} \in {1, 2}$ for $1 \leq i \leq n - 1$ . We prove that there are nearly consecutive sequences of length $…