Kamalesh Saha

activity

20212026

most citedOn the path ideals of chordal graphs

1 citations · 3 across the 25 of their papers we have counts for

collaborators

27 papers

math.AC2026

Componentwise linearity, Fröberg's analogue, and classification of linear support-two monomial ideals

Manohar Kumar, Kamalesh Saha

In this paper, we investigate the componentwise linear property of support-two monomial ideals. Our first main result shows that if $I$ is a support-two monomial ideal, then its un…

math.AC2025

Equality of ordinary and symbolic powers and the Conforti-Cornuéjols 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

Comparing the $v$ -number and $h$ -polynomials of edge ideals

Kamalesh Saha, Adam Van Tuyl

In this paper, we compare the $v$ -numbers and the degree of the $h$ -polynomials associated with edge ideals of connected graphs. We prove that the $v$ -number can…

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.AC2025

Square-free powers of Cohen-Macaulay simplicial forests

Kanoy Kumar Das, Amit Roy, Kamalesh Saha

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

math.CO2025

Stanley-Reisner ideals of higher independence complexes of chordal graphs

Kanoy Kumar Das, Amit Roy, Kamalesh Saha

For $t \geq 2$ , the $t$ -independence complex $Ind_{t} (G)$ of a graph $G$ is the collection of all $A \subseteq V (G)$ such that each connected component of the induced subgraph…

math.AC2024

Regularity of two classes of Cohen-Macaulay binomial edge ideals

Om Prakash Bhardwaj, Kamalesh Saha

Some recent investigations indicate that for the classification of Cohen-Macaulay binomial edge ideals, it suffices to consider biconnected graphs with some whiskers attached (in s…

math.AC2024★ 1 cited

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 $G$ …

math.AC2024

Binomial expansion and the $v$ -number

Kamalesh Saha

Let $I \subset A$ and $J \subset B$ be two monomial ideals, where $A$ and $B$ are two polynomial rings with disjoint variables. Considering a general set-up of monomial filtrations,…

math.CO2024★ 1 cited

On the path ideals of chordal graphs

Kanoy Kumar Das, Amit Roy, Kamalesh Saha

In this article, we give combinatorial formulas for the regularity and the projective dimension of $3$ -path ideals of chordal graphs, extending the well-known formulas for the edge…

math.AC2024

On the $v$ -number of binomial edge ideals of some classes of graphs

Deblina Dey, A. V. Jayanthan, Kamalesh Saha

Let $G$ be a finite simple graph, and $J_{G}$ denote the binomial edge ideal of $G$ . In this article, we first compute the $v$ -number of binomial edge ideals corresponding t…

math.AC2024

The slope of v-function and Waldschmidt constant

Manohar Kumar, Ramakrishna Nanduri, Kamalesh Saha

In this paper, we study the asymptotic behaviour of the v-number of a Noetherian graded filtration $I = {I_{[k]}}_{k \geq 0}$ of a Noetherian $N$ -graded domain $…

math.AC2024

Asymptotic behaviour and stability index of v-numbers of graded ideals

Prativa Biswas, Mousumi Mandal, Kamalesh Saha

Recently, Ficarra and Sgroi initiated the study of v-numbers of powers of graded ideals. They proved that for a graded ideal $I$ in a polynomial ring $S$ , $v (I^{k})$ is a li…

math.AC2024

On the Depth of Generalized Binomial Edge Ideals

Anuvinda J, Ranjana Mehta, Kamalesh Saha

This research focuses on analyzing the depth of generalized binomial edge ideals. We extend the notion of $d$ -compatible map for the pairs of a complete graph and an arbitrary grap…

math.AC2023

On the $v$ -number of Gorenstein ideals and Frobenius powers

Nirmal Kotal, Kamalesh Saha

In this paper, we show the equality of the (local) $v$ -number and Castelnuovo-Mumford regularity of certain classes of Gorenstein algebras, including the class of Gorenste…

math.AC2023

Componentwise linearity of edge ideals of weighted oriented graphs

Manohar Kumar, Ramakrishna Nanduri, Kamalesh Saha

In this paper, we study the componentwise linearity of edge ideals of weighted oriented graphs. We show that if $D$ is a weighted oriented graph whose edge ideal $I (D)$ is componen…

math.AC2023

The $v$ -number and Castelnuovo-Mumford regularity of cover ideals of graphs

Kamalesh Saha

The $v$ -number of a graded ideal $I \subseteq R$ , denoted by $v (I)$ , is the minimum degree of a polynomial $f$ for which $I : f$ is a prime ideal. Jaramillo and Vill…

math.AC2023

Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

Kamalesh Saha

Herzog, Hibi, and Zheng classified the Cohen-Macaulay edge ideals of chordal graphs. In this paper, we classify Cohen-Macaulay edge ideals of (vertex) weighted oriented chordal and…

math.AC2023

The $v$ -Number of Binomial Edge Ideals

Siddhi Balu Ambhore, Kamalesh Saha, Indranath Sengupta

The invariant $v$ -number was introduced very recently in the study of Reed-Muller-type codes. Jaramillo and Villarreal (J Combin. Theory Ser. A 177:105310, 2021) initiated…

math.AC2022

Cohen-Macaulay Property of Binomial Edge Ideals with Girth of Graphs

Kamalesh Saha, Indranath Sengupta

Conca and Varbaro (Invent. Math. 221 (2020), no. 3) showed the equality of depth of a graded ideal and its initial ideal in a polynomial ring when the initial ideal is square-free.…

math.AC2022

Cohen-Macaulay Binomial edge ideals in terms of blocks with whiskers

Kamalesh Saha, Indranath Sengupta

For a graph $G$ , Bolognini et al. have shown $J_{G}$ is strongly unmixed $\Rightarrow$ $J_{G}$ is Cohen-Macaulay $\Rightarrow$ $G$ is accessible, where $J_{G}$ denotes the binomial…

math.AC2022

Cohen-Macaulay Weighted Oriented Edge Ideals and its Alexander Dual

Kamalesh Saha, Indranath Sengupta

The study of the edge ideal $I (D_{G})$ of a weighted oriented graph $D_{G}$ with underlying graph $G$ started in the context of Reed-Muller type codes. We generalize a Cohen-Macaul…

Componentwise linearity, Fröberg's analogue, and classification of linear support-two monomial ideals

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

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

Comparing the v-number and h-polynomials of edge ideals

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 simplicial forests

Stanley-Reisner ideals of higher independence complexes of chordal graphs

Regularity of two classes of Cohen-Macaulay binomial edge ideals

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

Binomial expansion and the v-number

On the path ideals of chordal graphs

On the v-number of binomial edge ideals of some classes of graphs

The slope of v-function and Waldschmidt constant

Asymptotic behaviour and stability index of v-numbers of graded ideals

On the Depth of Generalized Binomial Edge Ideals

On the v-number of Gorenstein ideals and Frobenius powers

Componentwise linearity of edge ideals of weighted oriented graphs

The v-number and Castelnuovo-Mumford regularity of cover ideals of graphs

Cohen-Macaulay Weighted Oriented Chordal and Simplicial Graphs

The v-Number of Binomial Edge Ideals

Cohen-Macaulay Property of Binomial Edge Ideals with Girth of Graphs

Cohen-Macaulay Binomial edge ideals in terms of blocks with whiskers

Cohen-Macaulay Weighted Oriented Edge Ideals and its Alexander Dual

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

Comparing the $v$ -number and $h$ -polynomials of edge ideals

Binomial expansion and the $v$ -number

On the $v$ -number of binomial edge ideals of some classes of graphs

On the $v$ -number of Gorenstein ideals and Frobenius powers

The $v$ -number and Castelnuovo-Mumford regularity of cover ideals of graphs

The $v$ -Number of Binomial Edge Ideals