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

2005/03/17 by N. Frantzikinakis, Frantzikinakis, N., E. Lesigne +3 · 1 citation
Mathematics · #28D05 #37A45 #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #math.CO #math.DS #msc:28D05 #msc:37A45

paper · pdf · doi:10.48550/arxiv.math/0503367

8 pages

arxiv created 2005/04/05 · arxiv updated 2009/12/01

Abstract

For every k∈ 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 which is not 2-recurrent. We discuss a similar result for convergence of multiple ergodic averages. Finally, we also point out a combinatorial consequence related to Szemer' edi's theorem.

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• Multiple Polynomial Recurrence in Weyl Systems

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