Year: 2026
Type: preprint
Abstract: Fix $k,s\in\mathbb{N}$. We prove that there exists a subadditive density on $\mathbb{N}$ such that, for every polynomial $P\in\mathbb{Z}[y]$ of degree $k$ and with $P(0)=0$, every set of positive density contains configurations $\{x,x+P(y),xy^s\}$ for arbitrarily large $x>y\geq 2$. This provides a density strengthening of Moreira's result on partition regularity for $\{x,x+y,xy\}$.
Source: arXiv (Cornell University)
Authors: Richter, Florian K., Tsinas, Konstantinos
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214654194