Trung Nam Tran

activity

20122023

most citedDepth and regularity of powers of sums of ideals

52 citations · 186 across the 10 of their papers we have counts for

collaborators

11 papers

math.AC2023

A general formula for the index of depth stability of edge ideals

Ha Minh Lam, Ngo Viet Trung, Tran Nam Trung

By a classical result of Brodmann, the function $depth R / I^{t}$ is asymptotically a constant, i.e. there is a number $s$ such that $\operatorname{depth} R/I^t = \opera…

math.AC2019★ 14 cited

Depth functions of powers of homogeneous ideals

Huy Tai Ha, Hop Dang Nguyen, Ngo Viet Trung +1

We settle a conjecture of Herzog and Hibi, which states that the function depth $S / Q^{n}$ , $n \geq 1$ , where $Q$ is a homogeneous ideal in a polynomial ring $S$ , can be any convergent…

math.AC2019★ 15 cited

Regularity and Koszul property of symbolic powers of monomial ideals

Le Xuan Dung, Truong Thi Hien, Hop D. Nguyen +1

Let $I$ be a homogeneous ideal in a polynomial ring over a field. Let $I^{(n)}$ be the $n$ -th symbolic power of $I$ . Motivated by results about ordinary powers of $I$ , we study the…

math.AC2017★ 38 cited

Symbolic powers of sums of ideals

Huy Tai Ha, Dang Hop Nguyen, Ngo Viet Trung +1

Let $I$ and $J$ be nonzero ideals in two Noetherian algebras $A$ and $B$ over a field $k$ . Let $I + J$ denote the ideal generated by $I$ and $J$ in $A \otimes_{k} B$ . We prove the follo…

math.CO2016★ 2 cited

Coverings, Matchings and the number of maximal independent sets of graphs

Do Trong Hoang, Tran Nam Trung

We determine the maximum number of maximal independent sets of arbitrary graphs in terms of their covering numbers and we completely characterize the extremal graphs. As an applica…

math.CO2016

Buchsbaumness of the second powers of edge ideals

Do Trong Hoang, Tran Nam Trung

We graph-theoretically characterize the class of graphs $G$ such that $I (G)^{2}$ are Buchsbaum.

math.AC2016★ 36 cited

Stability of Depths of Powers of Edge Ideals

Tran Nam Trung

Let $G$ be a graph and let $I := I (G)$ be its edge ideal. In this paper, we provide an upper bound of $n$ from which $\depth R/ I(G)^n$ is stationary, and compute this limit expli…

math.AC2015★ 27 cited

A Characterization of Triangle-free Gorenstein graphs and Cohen-Macaulayness of second powers of edge ideals

Do Trong Hoang, Tran Nam Trung

We graph-theoretically characterize triangle-free Gorenstein graphs $G$ . As an application, we classify when $I (G)^{2}$ is Cohen-Macaulay.

math.AC2015★ 52 cited

Depth and regularity of powers of sums of ideals

Huy Tai Ha, Ngo Viet Trung, Tran Nam Trung

Given arbitrary homogeneous ideals $I$ and $J$ in polynomial rings $A$ and $B$ over a field $k$ , we investigate the depth and the Castelnuovo-Mumford regularity of powers of the su…

math.AC2014

Regularity of powers of forests and cycles

Selvi Kara, Huy Tai Ha, Tran Nam Trung

Let G be a graph and let I = I(G) be its edge ideal. In this paper, when G is a forest or a cycle, we explicitly compute the regularity of I^s for all s > 0. In particular, for the…

math.AC2012★ 2 cited

Cohen-Macaulay graphs with large girth

Dô Trong Hoang, Nguyên Cong Minh, Trân Nam Trung

We classify Cohen-Macaulay graphs of girth at least $5$ and planar Gorenstein graphs of girth at least $4$ . Moreover, such graphs are also vertex decomposable.