On Alweiss's example for multiple recurrence

Ben Green

On Alweiss's example for multiple recurrence

Dynamical Systems 2026-07-27 v1

Authors: Ben Green

Abstract

In this expository note we discuss the example of R.~Alweiss giving a construction of a set $S \subset \mathbf{N}$ which intersects every nil-Bohr set, but which is not a set of $2$ -recurrence.

Cite

@article{arxiv.2607.24594,
  title  = {On Alweiss's example for multiple recurrence},
  author = {Ben Green},
  journal= {arXiv preprint arXiv:2607.24594},
  year   = {2026}
}

Comments

6 pages, expository note. Not intended for publication