Rajiv Kumar

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math.AC2026

The Waldschmidt constant of square-free principal Borel ideals

Ajay Kumar, Rajiv Kumar, Paramhans Kushwaha

Fix a square-free monomial $m = x_{i_{1}} \dots x_{i_{s}}$ in $S = \K[x_1, \dots, x_n]$, where $\K$ is a field. The ideal generated by all square-free monomials that are Borel moves o…

math.AC2026

The Mendez-Pinto-Villarreal Conjecture for some classes of monomial ideals

Paromita Bordoloi, Kanoy Kumar Das, Rajiv Kumar

Characterizing when the symbolic and ordinary powers of an ideal coincide is a central problem in commutative algebra, and ideals satisfying this property are called Simis ideals.…

math.AC2025

Hilbert Coefficients and Regularity of Binomial Edge Ideals

Kanoy Kumar Das, Rajiv Kumar, Paramhans Kushwaha

Let $G$ be a simple graph on $n$ vertices, and let $J_{G}$ denotes the corresponding binomial edge ideal in $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ , where $K$ is a fie…

math.AC2025

Application of Betti Splittings to the Regularity of Binomial Edge Ideals

Rajiv Kumar, Paramhans Kushwaha

Let $G$ be a simple graph on $[n]$ vertices and $J_{G}$ denote the corresponding binomial edge ideal in $S = k [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}]$ , where $k$ is a field. In this paper, we…