22 citations · 51 across the 11 of their papers we have counts for
4 papers · 1 filter
The monomial ideal of a finite meet-semilattice
Juergen Herzog, Takayuki Hibi, Xinxian Zheng
Squarefree monomial ideals arising from finite meet-semilattices and their free resolutions are studied. For the squarefree monomial ideals corresponding to poset ideals in a distr…
Resolutions of facet ideals
Xinxian Zheng
In this paper we study the resolution of a facet ideal associated with a special class of simplicial complexes introduced by S. Faridi. These simplicial complexes are called trees,…
Dirac's theorem on chordal graphs and Alexander duality
Jürgen Herzog, Takayuki Hibi, Xinxian Zheng
By using Alexander duality on simplicial complexes we give a new and algebraic proof of Dirac's theorem on chordal graphs.
Monomial ideals whose powers have a linear resolution
Juergen Herzog, Takayuki Hibi, Xinxian Zheng
In this paper we consider graded ideals in a polynomial ring over a field and ask when such an ideal has the property that all of its powers have a linear resolution. In particular…