From the 1 of 8 linked papers with an AI index.
8 papers
Recurrence in a dynamical system over adequate partial semigroups
Md Moid Shaikh, Shivam Kumar, Sourav Kanti Patra
The paper studies quasi‑central sets in commutative adequate partial semigroups, providing algebraic and dynamical characterizations of the associated idempotent ultrafilters and i…
Ideal Zero-Product Probability in Finite Commutative Rings
Sukrit Chakraborty, Sourav Kanti Patra
We introduce the \emph{ideal zero-product probability}, a new probabilistic invariant associated with a finite commutative ring , defined by \[ ζ_k(R) = \frac{ |\{(I_1,\ldots,I_…
Monochromatic Sums and Quotients Near Zero
Md Moid Shaikh, Sourav Kanti Patra, Mukesh Kumar
Recently S. Goswami proved that whenever the set of natural numbers is finitely colored, the set is monochromatic which also established a varian…
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…
Graded Betti numbers of a hyperedge ideal associated to join of graphs
Sourav Kanti Patra, Amit Roy
Let be a finite simple graph on the vertex set and let be a positive integer. We consider the hypergraph whose vertices are the vertices of a…