منابع مشابه
New methods for constructing shellable simplicial complexes
A clutter $mathcal{C}$ with vertex set $[n]$ is an antichain of subsets of $[n]$, called circuits, covering all vertices. The clutter is $d$-uniform if all of its circuits have the same cardinality $d$. If $mathbb{K}$ is a field, then there is a one-to-one correspondence between clutters on $V$ and square-free monomial ideals in $mathbb{K}[x_1,ldots,x_n]$ as follows: To each clutter $mathcal{C}...
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Among shellable complexes a certain class has maximal modular homology, and these are the so-called saturated complexes. We extend the notion of saturation to arbitrary pure complexes and give a survey of their properties. It is shown that saturated complexes can be characterized via the p -rank of incidence matrices and via the structure of links. We show that rank-selected subcomplexes of sat...
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We first introduce the notion of a completion. Completions are inductive properties which may be expressed in a declarative way and which may be combined. We show that completions may be used for describing structures or transformations which appear in combinatorial topology. We present two completions, 〈CUP〉 and 〈CAP〉, in order to define, in an axiomatic way, a remarkable collection of acyclic...
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One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for StanleyReisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Goren...
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Definition 20 (simplex). A k-simplex σ is the convex hull of a set P of k + 1 affinely independent points. In particular, a 0-simplex is a vertex, a 1-simplex is an edge, a 2-simplex is a triangle, and a 3-simplex is a tetrahedron. A k-simplex is said to have dimension k. A face of σ is a simplex that is the convex hull of a nonempty subset of P. Faces of σ come in all dimensions from zero (σ’s...
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ژورنال
عنوان ژورنال: Illinois Journal of Mathematics
سال: 1997
ISSN: 0019-2082
DOI: 10.1215/ijm/1255985839