New Obstacles to Multiple Recurrence
arXiv:2511.21680
Abstract
We show that there is a set which is not a set of multiple recurrence despite being a set of recurrence for nil-Bohr sets. This answers Huang, Shao, and Ye's \enquote{higher-order} version of Katznelson's Question on Bohr recurrence and topological recurrence in the negative. Equivalently, we construct a set so that there is a finite coloring of without three-term arithmetic progressions with common differences in , but so that lacks the usual polynomial obstacles to arithmetic progressions.
13 pages, 1 figure, comments welcome!