The ACO Seminar (2022–2023)

We show that the pattern ${x,x+y,xy}$ is partition regular over the space of formal integer polynomials of degree at least one with zero constant term, with primitive recursive bounds. This provides a new proof for the partition regularity of ${x,x+y,xy}$ over $\mathbb N$, which obtains the first primitive recursive bound.

https://arxiv.org/abs/2211.00766