Arvind Kumar

activity

20162023

most citedRegularity of powers of quadratic sequences with applications to binomial ideals

22 citations · 77 across the 21 of their papers we have counts for

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17 papers · 1 filter

math.AC2023

Resurgence number of graded families of ideals

Tài Huy Hà, Arvind Kumar, Hop D. Nguyen +1

We define the resurgence and asymptotic resurgence numbers associated to a pair of graded families of ideals in a Noetherian ring. These notions generalize the well-studied resurge…

math.AC2021

Binomial expansion for saturated and symbolic powers of sums of ideals

Huy Tai Ha, A. V. Jayanthan, Arvind Kumar +1

There are two different notions for symbolic powers of ideals existing in the literature, one defined in terms of associated primes, the other in terms of minimal primes. Elaborati…

math.AC2021★ 1 cited

On the resurgence and asymptotic resurgence of homogeneous ideals

A. V. Jayanthan, Arvind Kumar, Vivek Mukundan

Let $K$ be a field and $R = K [x_{1}, \dots, x_{n}]$ . We obtain an improved upper bound for asymptotic resurgence of squarefree monomial ideals in $R$ . We study the e…

math.AC2021

Rees algebra and special fiber ring of binomial edge ideals of closed graphs

Arvind Kumar

In this article, we compute the regularity of Rees algebra of binomial edge ideals of closed graphs. We obtain a lower bound for the regularity of Rees algebra of binomial edge ide…

math.AC2020★ 3 cited

Regularity of parity binomial edge ideals

Arvind Kumar

Let $G$ be a simple graph on $n$ vertices and $I_{G}$ denotes parity binomial edge ideal of $G$ in the polynomial ring $S = K [x_{1}, \dots, x_{n}, y_{1}, \dots, y_{n}] .$ …

math.AC2020

Subadditivity, strand connectivity and multigraded Betti numbers of monomial ideals

A. V. Jayanthan, Arvind Kumar

Let $R = K [x_{1}, \dots, x_{n}]$ and $I \subset R$ be a homogeneous ideal. In this article, we first obtain certain sufficient conditions for the subadditivity of $R / I$ . As a…