14 papers
Monochromatic Translated Product and Answering Sahasrabudhe's Conjecture
Sayan Goswami
This article resolves two related problems in Ramsey theory on the integers. We show that for any finite coloring of the set of natural numbers, there exist numbers and for…
On difference sets of dense subsets of
Sayan Goswami
In this article, we study the structure of the difference set for subsets of positive upper Banach density. Fish asked in [Proc. Amer. Math. Soc.…
Random Finite Sumsets and Product Sets in Subsets of the Natural Numbers
Sukrit Chakraborty, Sayan Goswami, Sourav Kanti Patra
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of where…
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…
On Polynomial Extensions of van der Waerden's Theorem and its Applications
Sayan Goswami
In this article, we investigate polynomial generalizations of the van der Waerden theorem with a focus on largeness properties of recurrence patterns. We prove an -stre…
Nonlinear Kernel Partition Regularity: Necessary and Sufficient Conditions
Sayan Goswami
A matrix \( A \) is called \emph{kernel partition regular} if, for every finite coloring of the natural numbers \( \mathbb{N} \), there exists a monochromatic solution to the equat…