Edgewise strongly shellable clutters

Cohen-macaulay, Shellable and Unmixed Clutters with a Perfect Matching of König Type

Let C be a clutter with a perfect matching e1, . . . , eg of König type and let ∆C be the Stanley-Reisner complex of the edge ideal of C. If all c-minors of C have a free vertex and C is unmixed, we show that ∆C is pure shellable. We are able to describe in combinatorial terms when ∆C is pure. If C has no cycles of length 3 or 4, then it is shown that ∆C is pure if and only if ∆C is pure shella...

Graphical representations of clutters

We discuss the use of K-terminal networks to represent arbitrary clutters. A given clutter has many di¤erent representations, and there does not seem to be any set of simple transformations that can be used to transform one representation of a clutter into any other. We observe that for t 2 the class of clutters that can be represented using no more than t terminals is closed under minors, and ...

Ideal clutters

From Clutters to Matroids

This paper deals with the question of completing a monotone increasing family of subsets Γ of a finite set Ω to obtain the dependent sets of a matroid. Specifically, we provide several natural processes for transforming the clutter Λ of the inclusionminimal subsets of the family Γ into the set of circuits C(M) of a matroid M with ground set Ω. In addition, by combining these processes, we prove...

Criterions for Shellable Multicomplexes

After [4] the shellability of multicomplexes Γ is given in terms of some special faces of Γ called facets. Here we give a criterion for the shellability in terms of maximal facets. Multigraded pretty clean filtration is the algebraic counterpart of a shellable multicomplex. We give also a criterion for the existence of a multigraded pretty clean filtration.