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math.CO2009
An ultrafilter approach to Jin's Theorem
Mathias Beiglboeck
It is well known and not difficult to prove that if of integers has positive upper Banach density, the set of differences is syndetic, i.e. the length of gaps is uniforml…
math.CO2008
A Multidimensional Central Sets Theorem
Mathias Beiglböck
The Theorems of Hindman and van der Waerden belong to the classical theorems of partition Ramsey Theory. The Central Sets Theorem is a strong simultaneous extension of both theorem…