Thanh Vu

activity

20232026

collaborators

12 papers

math.AC2026

Associated primes and v-numbers of integral closures of powers of edge ideals

Trung Chau, Tai Huy Ha, Thanh Vu

Let $I = I (G)$ be the edge ideal of a finite simple graph $G$ . We investigate the relationship between the associated primes and $v$ -numbers of powers $I^{t}$ and their integral clos…

math.GT2026

$Z_{p}$ -folded surfaces and the $Z_{p}$ -Thurston norm

William Hobkirk

$Z_{p}$ -folded surfaces are a class of oriented folded surfaces with a fundamental $H_{2} (Z / p Z)$ class. In this paper we study the $Z_{p}$ -folded surf…

math.AC2026

Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals

Trung Chau, Tài Huy Hà, A. V. Jayanthan +1

Let $I$ be a squarefree monomial ideal, and let $d$ denote the maximum degree of a minimal generator of $I$ . We prove that \[ v(I^t)\le v(I^{(t)})+(t-1)(d-1) \] for all $t \geq 1$ , wh…

math.AC2026

V-numbers of powers of cover ideals of unimodular hypergraphs

Nguyen Thu Hang, Thanh Vu

Let $H$ be a unimodular hypergraph with cover ideal $J (H)$ . We prove that the local $v$ -numbers of $J (H)^{t}$ are linear in $t$ for all $t \geq 1$ . We further show that the global $v$ -n…

math.AC2026

Ordered alternating paths and the depth of symbolic powers of cover ideals of graphs

Nguyen Thu Hang, Nguyen Thi Thanh Tam, Thanh Vu

Let $G$ be a simple graph with cover ideal $J (G)$ in a polynomial ring $S$ in $∣ V (G) ∣$ variables. For a matching $M$ of $G$ , we denote by $ℓ (M)$ the length of the longest $M$ -al…

math.AC2026

Admissible subgraphs and the depth of symbolic powers of cover ideals of graphs

Tran Duc Dung, Nguyen Thu Hang, Thanh Vu

Let $G$ be a simple graph. We introduce the notion of $t$ -admissible subgraphs of $G$ and show how to use them to compute the depth of the $t$ -th symbolic powers of the cover ideal…

math.AC2026

Depth of powers of the edge ideal of an increasing weighted path

Jiaxin Li, Dancheng Lu, Thanh Vu +1

We provide exact formulas for the depth of the quotient ring of powers of the edge ideal of an increasing weighted path.

math.AC2024

Multiplicity of powers of squarefree monomial ideals

Phan Thi Thuy, Thanh Vu

Let $I$ be an arbitrary nonzero squarefree monomial ideal of dimension $d$ in a polynomial ring $S = k [x_{1}, \dots, x_{n}]$ . Let $μ$ be the number of associated primes of $S/I…

math.AC2024

Graded Betti numbers of powers of path ideals of paths

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $I_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n + 1} x_{n + 2} \dots x_{n + m})$ be the $m$ -path ideal of a path of length $n + m - 1$ over a polynomial ring $S = \mathrm{k}[…

math.AC2024

Betti numbers of powers of path ideals of cycles

Silviu Balanescu, Mircea Cimpoeas, Thanh Vu

Let $J_{n, m} = (x_{1} \dots x_{m}, x_{2} \dots x_{m + 1}, \dots, x_{n} x_{1} \dots x_{m - 1})$ be the $m$ -path ideal of a cycle of length $n \geq 5$ over a polynomial ring $S = k[x_1,\ldots,x_n…

math.AC2024

Projective dimension and regularity of 3-path ideals of unicyclic graphs

Nguyen Thu Hang, Thanh Vu

We compute the projective dimension and regularity of $3$ -path ideals of arbitrary graphs with at most one cycle.

math.AC2023

Depth of powers of edge ideals of Cohen-Macaulay trees

Nguyen Thu Hang, Truong Thi Hien, Thanh Vu

Let $I$ be the edge ideal of a Cohen-Macaulay tree of dimension $d$ over a polynomial ring $S = k [x_{1}, \dots, x_{d}, y_{1}, \dots, y_{d}]$ . We prove that for all $t \geq 1$ , $$\op…

Associated primes and v-numbers of integral closures of powers of edge ideals

Zp​-folded surfaces and the Zp​-Thurston norm

Comparing v-numbers of symbolic and ordinary powers of squarefree monomial ideals

V-numbers of powers of cover ideals of unimodular hypergraphs

Ordered alternating paths and the depth of symbolic powers of cover ideals of graphs

Admissible subgraphs and the depth of symbolic powers of cover ideals of graphs

Depth of powers of the edge ideal of an increasing weighted path

Multiplicity of powers of squarefree monomial ideals

Graded Betti numbers of powers of path ideals of paths

Betti numbers of powers of path ideals of cycles

Projective dimension and regularity of 3-path ideals of unicyclic graphs

Depth of powers of edge ideals of Cohen-Macaulay trees

$Z_{p}$ -folded surfaces and the $Z_{p}$ -Thurston norm