Sayan Goswami

collaborators

5 papers

math.CO2024

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…

math.CO2024

Restricted van der Waerden theorem for nilprogressions

Sayan Goswami

In [Adv. Math., 321 (2017) 269-286], using the theory of ultrafilters, J. H. Johnson Jr., and F. K. Richter proved the nilpotent polynomial Hales-Jewett theorem. Using this result…

math.DS2024

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…

math.CO2024

Monochromatic Polynomial sumset structures on $N$ : an ultrafilter proof

Sayan Goswami

Recently, using machinery's from Ergodic theory, Z. Lian, and R. Xiao proved if $P$ is any polynomial with no constant term, then for every finite coloring of $N$ , there e…

math.CO2023

Combined exponential patterns in multiplicative $I P^{⋆}$ sets

Pintu Debnath, Sayan Goswami

$I P$ sets play fundamental role in arithmetic Ramsey theory. A set is called an additive $I P$ set if it is of the form $FS\left(\langle x_{n}\rangle_{n\in \mathbb{N}}\right)=\left\…

Exponential Schur and Hindman Theorem in Ramsey Theory

Restricted van der Waerden theorem for nilprogressions

Dynamical characterization of central sets in adequate partial semigroups

Monochromatic Polynomial sumset structures on N: an ultrafilter proof

Combined exponential patterns in multiplicative IP⋆ sets

Monochromatic Polynomial sumset structures on $N$ : an ultrafilter proof

Combined exponential patterns in multiplicative $I P^{⋆}$ sets