146 citations · 377 across the 33 of their papers we have counts for
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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…
Distributive Lattices, Bipartite Graphs and Alexander Duality
Juergen Herzog, Takayuki Hibi
A certain squarefree monomial ideal arising from a finite partially ordered set will be studied from viewpoints of both commutative algebra and combinatorics. First, it i…
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…
Rigid resolutions and big Betti numbers
Aldo Conca, Juergen Herzog, Takayuki Hibi
In the first part of the paper we answer (positively) a question raised by the first author which has to do with some sort of rigity of the tail of resolution of an ideal. Let …