A. Roy

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20242026

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math.AC2025

Equality of ordinary and symbolic powers and the Conforti-CornuÃ©jols conjecture for $(n - 2)$ -uniform clutters

Amit Roy, Kamalesh Saha

Let $I$ be an equigenerated squarefree monomial ideal in the polynomial ring $K [x_{1}, \dots, x_{n}]$ , and let $H$ be a uniform clutter on the vertex set $\{x_1,\ldot…

math.AC2025

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers

Trung Chau, Kanoy Kumar Das, Amit Roy +1

We introduce the abstract notion of squarefree-power-like functions, which unify the sequences of squarefree ordinary and symbolic powers of squarefree monomial ideals. By employin…

math.AC2025

Square-free powers of Cohen-Macaulay simplicial forests

Kanoy Kumar Das, Amit Roy, Kamalesh Saha

Let $I (I^)^{[k]}$ denote the $k^{th}$ square-free power of the facet ideal of a simplicial complex $I^$ in a polynomial ring $R$ . Square-free powers are intimately related t…

math.AC2025

On the homological shifts of cover ideals of Cohen-Macaulay graphs

Amit Roy, Kamalesh Saha

For a non-negative integer $k$ , let $HS_{k} (J (G))$ denote the $k^{th}$ homological shift ideal of the vertex cover ideal $J (G)$ of a graph $G$ . For each $k \geq 2$ ,…

math.AC2025

Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers

Trung Chau, Kanoy Kumar Das, Amit Roy +1

Let $I$ be any square-free monomial ideal, and $H_{I}$ denote the hypergraph associated with $I$ . Refining the concept of $k$ -admissible matching of a graph defined by Erey…

math.AC2024

Square-free powers of Cohen-Macaulay forests, cycles, and whiskered cycles

Kanoy Kumar Das, Amit Roy, Kamalesh Saha

Let $I (G)^{[k]}$ denote the $k^{t h}$ square-free power of the edge ideal $I (G)$ of a graph $G$ . In this article, we provide a precise formula for the depth of $I (G)^{[k]}$ when $G$ …

Equality of ordinary and symbolic powers and the Conforti-CornuÃ©jols conjecture for (n−2)-uniform clutters

Admissible set and squarefree-power-like function with applications to squarefree symbolic powers

Square-free powers of Cohen-Macaulay simplicial forests

On the homological shifts of cover ideals of Cohen-Macaulay graphs

Admissible matchings and the Castelnuovo-Mumford regularity of square-free powers

Square-free powers of Cohen-Macaulay forests, cycles, and whiskered cycles

Equality of ordinary and symbolic powers and the Conforti-CornuÃ©jols conjecture for $(n - 2)$ -uniform clutters