M. A. Tootkaboni

collaborators

3 papers

math.CO2025

An Algebraic Proof of the Polynomial Version of van der Waerden's Theorem

Javad Jafari, Mohammad Akbari Tootkaboni

The polynomial version of van der Waerden's theorem, proved using dynamical systems by V. Bergelson and A. Leibman in 1996, \cite{Bergelson1996}, significantly highlighted the role…

math.CO2025

Polynomial extension of Van der Waerden's Theorem near zero

Ghadir Ghadimi, Mohammad Akbari Tootkaboni

Let $S$ be a dense subring of the real numbers. In this paper we prove a polynomial version of Van der Waerden's theorem near zero. In fact, we prove that if $p_1,\ldots,p_m \in \m…

math.CO2024

Partial semigroup partial dynamical systems and Partial Central Sets

H. Goodarzi, M. A. Tootkaboni, Arpita Ghosh

H. Furstenberg defined Central sets in $N$ by using the notions of topological dynamics, later Bergelson and Hindman characterized central sets in $N$ and also in…