arXiv subjects

Tran Quang Hoa

Publications and source records attributed to Tran Quang Hoa.

4 recordsLinked to original sources

arXiv2026

Independence polynomials and the weak Lefschetz property for tadpole graphs

Let $T_{m,n}$ be the tadpole graph obtained by joining a cycle $C_m$ to a path $P_n$ by a bridge. We prove that the independence polynomial of every tadpole graph is unimodal and establish sharp bounds for its mode. The unimodality result follows from a general criterion for graphs obtained by attaching a path to a fixed vertex. Over a field of characteristic zero, we also give a complete classification of the pairs $(m,n)$ for which the Artinian algebra defined by the edge ideal of $T_{m,n}$ together with the squares of all variables has the weak Lefschetz property.

math.AC↗

arXiv2025

The Weak Lefschetz Property for Tensor Products of Artinian Monomial Algebras and Its Applications to Lollipop Graphs

In this paper, we investigate the weak Lefschetz property for tensor products of Artinian monomial algebras and complete quadratic monomial algebras. As an application, we classify the weak Lefschetz property of the Artinian algebras $A(L_{m,n})$, which are defined by the edge ideals of the lollipop graphs $L_{m,n}$ together with the squares of the variables.

math.AC↗

arXiv2024

Asymptotic depth of invariant chains of edge ideals

We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of increasing functions on the positive integers. Our results and their proofs also reveal surprising combinatorial and topological properties of corresponding graphs and their independence complexes. In particular, we are able to determine the asymptotic behavior of all reduced homology groups of these independence complexes.

math.AC↗

arXiv2020

Fibers of rational maps and Rees algebras of their base ideals

We consider a rational map $ϕ: \mathbb{P}_k^{m} \dashrightarrow \mathbb{P}_k^n$ that is a parameterization of an $m$-dimensional variety. Our main goal is to study the $(m-1)$-dimensional fibers of $ϕ$ in relation to the $m$-th local cohomology modules of the Rees algebra of its base ideal.

math.AC↗