11 papers
Some new symmetric structures in Ramsey theory
Aninda Chakraborty, Sayan Goswami
In this article, we will investigate several new configurations in Ramsey Theory, using the $\ostar_{l,k}$-operation on the set of integers, recently introduced in \cite{key-4}. Th…
An abstract formulation of image partition regularity
Aninda Chakraborty, Sayan Goswami
Inspired by the paper [1] of V. Bergelson, John H.Johnson Jr., J. Moreira, we formulate an abstract version of image partition regularity. To establish the result we have used a va…
An analogue to infinitery Hales-Jewett theorem
Aninda Chakraborty, Sayan Goswami
In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. In this paper we wi…
Combined Algebraic Properties in Gaussian and Quaternion Ring
Aninda Chakraborty
It is known that for an IP^{*} set A in (\mathbb{N},+) and a sequence \left\langle x_{n}\right\rangle _{n=1}^{\infty} in \mathbb{N}, there exists a sum subsystem \left\langle y_{n}…
Abundance of Matrices In Gaussian Integers
Aninda Chakraborty
In [HLS], N. Hindman, I. Leader and D. Strauss proved the abundance for a matrix with rational entries. In this paper we proved it for the ring of Gaussian integers. We showed the…
Hales-Jewett type configurations in small sets
Aninda Chakraborty, Sayan Goswami
In a recent work, N. Hindman, D. Strauss and L. Zamboni have shown that the Hales-Jewett theorem can be combined with a sufficiently well behaved homomorphisms. Their work was comp…
Polynomial central set theorem near zero
Aninda Chakraborty, Sayan Goswami
N. Hindman and I. Leader introduced the set of ultrafilters 0+ on (0,1) and characterize smallest ideal of (0+,+) and proved the Central Set Theorem near zero. Recently Polynomial…
set in product space of countable adequate commutative partial semigroups
Aninda Chakraborty
A partial semigroup is a set with restricted binary operation. In this work we will extend a result due to V. Bergelson and N. Hindman concerning the rich structure presented in th…
Sets with arithmetic progressions are abundant
Aninda Chakraborty, Sayan Goswami
Furstenberg, Glasscock, Bergelson, Beiglboeck have been studied abundance in arithmatic progression on various large sets like piecewise syndetic, central, thick, etc. but also the…
Richness of arithmetic progression in commutative semigroup
Aninda Chakraborty, Sayan Goswami
Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise syndetic set contains k term arithmetic progressions and such collection is also piecewise syndetic in Z:…
Estimation of recurrence for nilpotent group action
Aninda Chakraborty, Dibyendu De, Sayan Goswami
We estimate size of recurrence of an action of a nilpotent group by homeomorphisms of a compact space for polynomial mappings into a nilpotent group form the partial semigroup $(\m…