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math.CO2026
-large sets are sets of nil-Bohr recurrence
Ryan Alweiss, Sohail Farhangi
A set of positive integers is -large if every two-coloring contains arbitrarily long monochromatic arithmetic progressions with common difference in . We prove that every…
math.DS2026
Solutions to 6 problems in recurrence and Van der Corput sets
Sohail Farhangi, Saúl Rodríguez Martín
We present solutions to six problems concerning sets of nice recurrence and van der Corput (vdC) sets. We answer a question of Moreira, repeated by Fish and Skinner, by showing tha…
math.DS2026
Multipliers and Disjointness from Mixing
Sohail Farhangi, Joel Moreira, Rigoberto Zelada
In 2005, Parreau proved that if a measure preserving system is not strongly mixing then it contains a non-trivial factor that is disjoint from every strongly mixing system. Taking…