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math.CO2026
Recurrence in a dynamical system over adequate partial semigroups
Md Moid Shaikh, Shivam Kumar, Sourav Kanti Patra
Using tools from topological dynamics, H.~Furstenberg introduced the notion of \emph{central sets} and established the celebrated Central Sets Theorem. The sets which satisfy the c…
math.AC2026
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_…
math.CO2026
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…