T. Chau

activity

20222026

most citedBarile-Macchia resolutions

7 citations · 8 across the 29 of their papers we have counts for

collaborators

33 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.AC2026

Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs

Trung Chau, Tran Quang Hoa, Dang Thi Kieu Uyen

Let $G$ be a finite simple graph and let $A_{c} (G)$ be the Artinian algebra associated with its cover ideal. We prove that $A_{c} (G)$ has the WLP when $τ (G) > ∣ V (G) ∣/2$ , where $τ (G)$ den…

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.CO2026

Multiplicity of negative one of independence polynomials of graphs

Om Prakash Bhardwaj, Trung Chau, Sayeed Ikram +3

We initiate the study of the multiplicity of negative one of independence polynomials of graphs. In this article, we simply refer to this as the \emph{multiplicity} of a graph. As…

math.AC2026

Golod ideals in combinatorial commutative algebra

Benjamin Briggs, Trung Chau, Alessandro De Stefani

In this article we study the Golod property of standard graded algebras. We show that determinantal ideals, binomial edge ideals, and permanental ideals are Golod if and only if th…

math.AC2026

The v-numbers of permanental ideals

Trung Chau, A. V. Jayanthan

In this article, we compute the $\vv$-number of $2 \times 2$ permanental ideals of generic, generic symmetric, and generic Hankel matrices.

math.GT2026

On Legendrian Thurston-Bennequin-symmetrical graphs

Trung Chau, Tanushree Shah

This article reviews the development of Legendrian graph theory in the standard contact 3-sphere ( $S^{3}, ξ_{s t d}$ ). We provide a generalized criterion under which the total Thurston…

math.AC2026

On licci squarefree monomial ideals

Om Prakash Bhardwaj, Trung Chau, Omkar Javadekar

We study the licci property for several classes of squarefree monomial ideals arising from graphs and related combinatorial structures. We characterize licci bi-Cohen-Macaulay squa…

math.AC2026

Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials

Jennifer Biermann, Trung Chau, Selvi Kara +4

Let $G$ be a finite simple graph on $n$ vertices and set $R = k [x_{1}, \dots, x_{n}]$ , with edge ideal $I (G)$ and cover ideal $J (G)$ . We give an explicit description of the $h$ -polynom…

math.AC2026

Symbolic powers and integral closures via extremal ideals

Trung Chau, Art Duval, Sara Faridi +3

This paper demonstrates that extremal ideals can be used to great effect to compute integral closures of powers and symbolic powers of square-free monomial ideals. We show that the…

math.AC2025

On Gotzmann thresholds and a conjecture of Bonanzinga and Eliahou

Trung Chau

We obtain a recursive formula for the Gotzmann threshold of a power of a variable. Consequently, we give an affirmative answer to a conjecture of Bonanzinga and Eliahou.

math.AC2025

Scarf complexes of connected and path ideals

Trung Chau, Richie Sheng, Tim Tribone +1

The $t$ -connected ideal of a graph $G$ is generated by all connected induced subgraphs of $G$ with $t$ vertices. When $t = 2$ , this coincides with the usual edge ideal of the graph…

math.AC2025

From neural codes to homological invariants: regularity and projective dimension of polarized neural ideals

Trung Chau

Neural codes form an algebraic framework to study the nervous system, and understanding neural codes is a key goal of mathematical neuroscience. Neural rings and ideals are the too…

math.AC2025

Projective monomial curves associated to numerical semigroups with multiplicity $e$ , width $e - 1$ , and embedding dimension $e - 2$

Om Prakash Bhardwaj, Trung Chau, Omkar Javadekar

Numerical semigroups with multiplicity $e$ , width $e - 1$ , and embedding dimension $e - 2$ are of the form $$S(e,m,n) = \langle \{e, e+1, \ldots, 2e-1\} \setminus \{e+m, e+n\} \rangle,…

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

The $F$ -singularities of algebras defined by permanents

Trung Chau

Let $X$ be a matrix of indeterminates, $t$ an integer, and $P_{t} (X)$ define the ideal generated by the permanents of all $t \times t$ submatrix of $X$ . $P_{t} (X)$ is called a permanent…

math.AC2025

Extremal behavior of ideals of minors

Trung Chau, Michael DeBellevue, Souvik Dey +2

Let $(R, m, k)$ be either a fiber product or an artinian stretched Gorenstein ring, with $ch (k) \neq = 2$ in the latter case. We prove that the…

math.AC2025

Maximal minors of $1$ -generic matrices have rational singularities

Trung Chau, Manoj Kummini

We show that the quotient ring by the ideal of maximal minors of a $1$ -generic matrix has rational singularities. This answers a conjecture of Eisenbud (1988) that such rings are n…

math.AC2025

Trees whose path ideals have linear quotients

Trung Chau, Kanoy Kumar Das, Animikha Dutta Dhar +2

For any integer $n$ , we classify all trees whose $n$ -path ideals have linear quotients.

math.AC2025

Permanental ideals of symmetric matrices

Trung Chau

In this article, we study the ideal generated by $2 \times 2$ permanents of a symmetric matrix. We denote this ideal by $P_{2} (X)$ where $X$ is a symmetric matrix. We compute a Gröbne…

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

Homological invariants of edge ideals of weighted oriented graphs

Trung Chau, Richie Sheng, Deborah Wooton

We determine all possible triples of depth, dimension, and regularity of edge ideals of weighted oriented graphs with a fixed number of vertices. Also, we compute all the possible…

math.AC2025

The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs

Trung Chau, Nursel Erey, Aryaman Maithani

Every monomial ideal $I$ has a Scarf complex, which is a subcomplex of its minimal free resolution. We say that $I$ is Scarf if its Scarf complex is also its minimal free resolutio…

math.AC2025

Edge ideals with linear quotients and without homological linear quotients

Trung Chau, Kanoy Kumar Das, Aryaman Maithani

A monomial ideal $I$ is said to have homological linear quotients if for each $k \geq 0$ , the homological shift ideal $HS_{k} (I)$ has linear quotients. It is a well-known fac…

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

Weak and strong Lefschetz properties for vertex cover Artinian algebras associated to graphs

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

Multiplicity of negative one of independence polynomials of graphs

Golod ideals in combinatorial commutative algebra

The v-numbers of permanental ideals

On Legendrian Thurston-Bennequin-symmetrical graphs

On licci squarefree monomial ideals

Realizable (reg, deg h)-Pairs for Cover Ideals via Independence Polynomials

Symbolic powers and integral closures via extremal ideals

On Gotzmann thresholds and a conjecture of Bonanzinga and Eliahou

Scarf complexes of connected and path ideals

From neural codes to homological invariants: regularity and projective dimension of polarized neural ideals

Projective monomial curves associated to numerical semigroups with multiplicity e, width e−1, and embedding dimension e−2

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

The F-singularities of algebras defined by permanents

Extremal behavior of ideals of minors

Maximal minors of 1-generic matrices have rational singularities

Trees whose path ideals have linear quotients

Permanental ideals of symmetric matrices

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

Homological invariants of edge ideals of weighted oriented graphs

The Scarf complex of squarefree powers, symbolic powers of edge ideals, and cover ideals of graphs

Edge ideals with linear quotients and without homological linear quotients

Projective monomial curves associated to numerical semigroups with multiplicity $e$ , width $e - 1$ , and embedding dimension $e - 2$

The $F$ -singularities of algebras defined by permanents

Maximal minors of $1$ -generic matrices have rational singularities