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Abundance of arithmetic progressions in -sets
Dibyendu De, Pintu Debnath
H.Furstenberg and E.Glasner proved that for an arbitrary , any piecewise syndetic set of integers contains a -term arithmetic progression and the collection of s…
Centrally Image partition Regularity near 0
Tanushree Biswas, Dibyendu De, Ram Krishna Paul
The notion of Image partition regularity near zero was first introduced by De and Hindman. It was shown there that like image partition regularity over the main source…
Additive and multiplicative structure of c-sets
Dibyendu De
It is known that for an IP set in and a sequence there exists a sum subsystem of $< x_{n}>_{n=1}^{\in…
Combined algebraic and multiplicative properties near zero
Dibyendu De, Ram Krishna Paul
It was proved that whenever is partitioned into finitely many cells, one cell must contain arbitrary length arithmetic and geometric progression nicely intertwined, so…