22 citations · 50 across the 10 of their papers we have counts for
10 papers
The depth of powers of an ideal
Juergen Herzog, Takayuki Hibi
We study the limit and initial behavior of the numerical function $f(k)=\depth S/I^k$. General properties of this function together with concrete examples arising from combinatoric…
Cohen-Macaulay Polymatroidal Ideals
Juergen Herzog, Takayuki Hibi
All Cohen--Macaulay polymatroidal ideals are classified. The Cohen--Macaulay polymatroidal ideals are precisely the principal ideals, the Veronese ideals, and the squarefree Verone…
Cohen-Macaulay chordal graphs
Juergen Herzog, Takayuki Hibi, Xinxian Zheng
We classify all Cohen-Macaulay chordal graphs. In particular. it is shown that a chordal graph is Cohen-Macaulay if and only if its unmixed.
Level rings arising from meet-distributive meet-semilattices
Juergen Herzog, Takayuki Hibi
The Alexander dual of an arbitrary meet-semilattice is described explicitly. Meet-distributive meet-semilattices whose Alexander dual is level are characterized.
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…
Discrete Polymatroids
Juergen Herzog, Takayuki Hibi
The discrete polymatroid is a multiset analogue of the matroid. Based on the polyhedral theory on integral polymatroids developed in late 1960's and in early 1970's, in the present…