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math.CO2026
Some monochromatic patterns in natural numbers
Arpita Ghosh, Surojit Ghosh
The set of sums of two squares plays a significant role in elementary number theory. In this article, we establish the existence of several rich monochromatic configurations in the…
math.CO2025
Combinatorially rich sets in partial semigroups
Arpita Ghosh, Neil Hindman
There are several notions of size for semigroups that have natural analogues for partial semigroups. Among these are thick, syndetic, central, piecewise syndetic, IP, J, and the mo…
math.CO2024
Partial semigroup partial dynamical systems and Partial Central Sets
H. Goodarzi, M. A. Tootkaboni, Arpita Ghosh
H. Furstenberg defined Central sets in by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in and also in…