22 citations · 50 across the 10 of their papers we have counts for
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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…