Sets of k-recurrence but not (k+1)-recurrence

N. Frantzikinakis, E. Lesigne, M. Wierdl

For every $k\in \mathbb{N}$, we produce a set of integers which is $k$-recurrent but not $(k+1)$-recurrent. This extends a result of Furstenberg who produced a 1-recurrent set whic…