Ri-Xiang Chen | Searcharxiv

arXiv2019

Lcm-lattice, Taylor Bases and Minimal Free Resolutions of a Monomial ideal

We use the lcm-lattice of a monomial ideal to study its minimal free resolutions. A new concept called a Taylor basis of a minimal free resolution is introduced and then used throughout the paper. We give a method of constructing minimal free resolutions of a monomial ideal from its lcm-lattice, which is called the atomic lattice resolution theory. Some applications of this theory is given. As the main application, we rewrite the theory of poset resolutions, and we obtain an approximation formula for minimal free resolutions of all monomial ideals.

math.AC↗

arXiv2015

On Two Classes of Regular Sequences

In this paper we get two new classes of regular sequences in the polynomial ring over the field of complex numbers.

math.AC↗

arXiv2014

How to compute the Hilbert depth of a graded ideal

We give two algorithms for computing the Hilbert depth of a \emph{graded ideal} in the polynomial ring. These algorithms work efficiently for (squarefree) lex ideals. As a consequence, we construct counterexamples to some conjectures made by Shen in \cite{B:Sh2}.

math.AC↗