Mousumi Mandal

activity

20232026

collaborators

7 papers

math.AC2026

A comparison of the v-number of a monomial ideal and its integral closure

Prativa Biswas, Mousumi Mandal, Partha Phukan

Let $I$ be a monomial ideal in a standard graded polynomial ring and let $I$ denote its integral closure. We study the relationship between $v (I)$ and $\mathrm{…

math.AC2026

Bounds on the second Hilbert coefficient and the depth of the associated graded ring

Clare D'Cruz, Mousumi Mandal, Shruti Priya

Let $(R, m)$ be a Noetherian local ring of dimension $d \geq 1$ with $depth R \geq d - 1,$ and let $I$ be an $m$ -primary ideal. In this paper, we study b…

math.AC2026

Asymptotic $v$ -number of graded families of ideals and the Newton-Okounkov region

Mousumi Mandal, Partha Phukan

In this paper, we prove that for Noetherian graded families $I = {I_{k}}_{k \geq 0}$ of homogeneous ideals in a Noetherian $N$ -graded Noetherian domain, $\lim\lim…

math.AC2026

Lattice points arising from regularity and $v$ -number of Graphs: Whisker and Cameron-Walker

Prativa Biswas, Mousumi Mandal, Kamalesh Saha

Let $G$ be a simple graph on $n$ vertices and $I (G) \subseteq R$ be its edge ideal. In this paper, we initiate the study of determining lattice points in $N^{2}$ that appear…

math.AC2024

Bounds on the Ratliff-Rush Index and the Castelnuovo-Mumford Regularity

Mousumi Mandal, Shruti Priya

Let $(R, m)$ be a Cohen-Macaulay local ring of dimension $d \geq 2,$ and $I$ an $m$ -primary ideal of $R .$ Denote $r_{J} (I)$ as the reduction number of $I$ with…

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.AC2023

A note on Ratliff-Rush filtration, reduction number and postulation number of $m$ -primary ideals

Mousumi Mandal, Shruti Priya

Let $(R, m)$ be a Cohen-Macaulay local ring of dimension $d \geq 2$ and $I$ an $m$ -primary ideal. Let rd $(I)$ be the reduction number of $I$ and n $(I)$ the postul…

A comparison of the v-number of a monomial ideal and its integral closure

Bounds on the second Hilbert coefficient and the depth of the associated graded ring

Asymptotic v-number of graded families of ideals and the Newton-Okounkov region

Lattice points arising from regularity and v-number of Graphs: Whisker and Cameron-Walker

Bounds on the Ratliff-Rush Index and the Castelnuovo-Mumford Regularity

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

A note on Ratliff-Rush filtration, reduction number and postulation number of m-primary ideals

Asymptotic $v$ -number of graded families of ideals and the Newton-Okounkov region

Lattice points arising from regularity and $v$ -number of Graphs: Whisker and Cameron-Walker

A note on Ratliff-Rush filtration, reduction number and postulation number of $m$ -primary ideals