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Recent Posts
- Erdős Sumset conjecture
- An arithmetic van der Corput trick and the polynomial van der Waerden theorem
- Piecewise syndetic sets, topological dynamics and ultrafilters
- Measure preserving actions of affine semigroups and {x+y,xy} patterns
- Szemerédi Theorem Part VI – Dichotomy between weak mixing and compact extension
Tag Archives: piecewise syndetic
An arithmetic van der Corput trick and the polynomial van der Waerden theorem
The van der Corput difference theorem (or trick) was develop (unsurprisingly) by van der Corput, and deals with uniform distribution of sequences in the torus. Theorem 1 (van der Corput trick) Let be a sequence in a torus . If … Continue reading
Piecewise syndetic sets, topological dynamics and ultrafilters
In this post I explore the notion of piecewise syndeticity and its relation to topological dynamical systems and the Stone-Čech compactification. I restrict attention to the additive semigroup but most results presented are true in much bigger generality (and I … Continue reading
Posted in Classic results, Combinatorics, Tool, Topological Dynamics
Tagged piecewise syndetic, recurrence, Ultrafilters
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