arXiv subjects
Publications and source records attributed to Hsin-Ju Wang.
Let $R$ be a commutative ring and $Γ(R)$ denote its zero-divisor graph. In this paper, we investigate the genus number of the compact Riemann surface which $Γ(R)$ can be embedded and illustrate all finite commutative rings $R$ (up to isomorphism) such that $Γ(R)$ is either toroidal or planar.
In this paper, we study various properties of matroidal ideals.
In this paper, we study the genera of zero-divisor graphs with respect to ideals in finite rings.
Let $G$ be a graph, $χ(G)$ be the minimal number of colors which can be assigned to the vertices of $G$ in such a way that every two adjacent vertices have different colors and $ω(G)$ to be the least upper bound of the size of the complete subgraphs contained in $G$. It is well-known that $χ(G)\geq ω(G)$. Beck in \cite{b} conjectured that $χ(Γ_0(R))=ω(Γ_0(R))$ if $ω(Γ_0(R))<\infty$, where $Γ_0(R)$ is a graph associated to a commutative ring $R$. In this note, we provide some sufficient conditions for a ring $R$ to enjoy $χ(Γ_0(R))=ω(Γ_0(R))$. As a consequence, we verify Beck's conjecture for the homomorphic image of $\mathbb{Z}^n$.
Let R be a standard graded ring over a commutative Noetherian ring with unity and I a graded ideal of R. Let M be a finitely generated graded R-module. We prove that there exist integers e and ρ_M(I) such that for all large n, reg(I^nM)= ρ_M(I)n+e.
In this paper, we give an affirmative answer to a conjecture raised by Polini and Ulrich.
In this paper, we derive several formulas of counting families of non-intersecting paths for two-sided ladder-shaped regions. As an application, we give a new proof to a combinatorial interpretation of Fibonacci numbers obtained by G. Andrews in 1974.
A formula concerning counting of paths was conjectured by Herzog and Conca few years ago. Recently, Krattenthaler and Prohaska gave an affirmative answer to this conjecture. In this paper we generalize this formula.