10 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…
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…