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Exponential Schur and Hindman Theorem in Ramsey Theory
Sayan Goswami, Sourav Kanti Patra
Answering a conjecture of A. Sisto, J. Sahasrabudhe proved the exponential version of the Schur theorem: for every finite coloring of the naturals, there exists a monochromatic cop…
Monocromaticity of additive and multiplicative central sets and Goswami's theorem in large Integral Domains
Pintu Debnath, Sourav Kanti Patra
In \cite{Fi} A. Fish proved that if and are two subsets of of positive upper Banach density, then there exists such that $…
Dynamical characterization of central sets in adequate partial semigroups
Pintu Debnath, Sayan Goswami, Sourav Kanti Patra
Using the methods from topological dynamics, H. Furstenberg introduced the notions of Central sets and proved the famous Central Sets Theorem which is the simultaneous extension of…
Multidimensional Stronger Central Sets Theorem and its Polynomial Extension
Sayan Goswami, Sourav Kanti Patra
We establish and fully characterize the multidimensional extension of the Stronger Central Sets Theorem. Additionally, we develop a polynomial generalization of this result. Our ap…
Large sets near idempotent and its product
Surajit Biswas, Sourav Kanti Patra
Tootkaboni and Vahed introduced the notion of some large sets near idempotent along with some combinatorial properties. We characterize when the finite Cartesian product of central…
The interplay between additive and symmetric large sets and their combinatorial applications
Arkabrata Ghosh, Sayan Goswami, Sourav Kanti Patra
The study of symmetric structures is a new trend in Ramsey theory. Recently in [7], Di Nasso initiated a systematic study of symmetrization of classical Ramsey theoretical results,…