${\mathrm{IP}}_{\mathrm{rat}}$-polynomial recurrence and large intersections

Borys Holikov, Or Shalom

Let $p_1,...,p_k$ be a rationally independent sequence of integer valued nonlinear polynomials. We show that for all $E\subseteq \mathbb{N}$, every Folner sequence $\hat{I}¦$, and every…