4 papers
Arithmetic subtrees in large subsets of products of trees
Kamil Bulinski, Alexander Fish
Furstenberg-Weiss have extended Szemerédi's theorem on arithmetic progressions to trees by showing that a large subset of the tree contains arbitrarily long arithmetic subtrees. We…
Reconstructing a minimal topological dynamical system from a set of return times
Kamil Bulinski, Alexander Fish
We investigate to what extent a minimal topological dynamical system is uniquely determined by a set of return times to some open set. We show that in many situations this is indee…
Glasner property for unipotently generated group actions on tori
Kamil Bulinski, Alexander Fish
A theorem of Glasner from 1979 shows that if is infinite then for each there exists an integer such that is -dense…
Twisted Recurrence via Polynomial Walks
Kamil Bulinski, Alexander Fish
In this paper we show how polynomial walks can be used to establish a twisted recurrence for sets of positive density in . In particular, we prove that if $Γ\leq \ope…