Ryan Alweiss

collaborators

3 papers

math.CO2026

$2$ -large sets are sets of nil-Bohr recurrence

Ryan Alweiss, Sohail Farhangi

A set $S$ of positive integers is $2$ -large if every two-coloring contains arbitrarily long monochromatic arithmetic progressions with common difference in $S$ . We prove that every…

math.CO2025

$2$ -large sets are sets of Bohr recurrence

Ryan Alweiss

Let $α_{1}, \dots, α_{d}$ be real numbers, fix $δ > 0$ , and let $S$ be the set of positive integers $s$ such that $∥ α_{i} s ∥_{R / Z} > δ$ for some $1 \leq i \leq d$ . We prove that $S$ is not \e…

math.DS2025

New Obstacles to Multiple Recurrence

Ryan Alweiss

We show that there is a set which is not a set of multiple recurrence despite being a set of recurrence for nil-Bohr sets. This answers Huang, Shao, and Ye's \enquote{higher-order}…

2-large sets are sets of nil-Bohr recurrence

2-large sets are sets of Bohr recurrence

New Obstacles to Multiple Recurrence

$2$ -large sets are sets of nil-Bohr recurrence

$2$ -large sets are sets of Bohr recurrence