Local properties of simplicial complexes

Hereditary properties and obstructions of simplicial complexes

In this paper, we discuss the relation between shellability, sequentially CohenMacaulayness, and partitionability. Especially, our main concern is to see the difference of these properties when we require heredity. For a property P, we say a simplicial complex satisfies hereditary-P if the simplicial complex itself and all the restrictions to subsets of its vertex set satisfy the property P, an...

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}...

Minors of simplicial complexes

We extend the notion of a minor from matroids to simplicial complexes. We show that the class of matroids, as well as the class of independence complexes, is characterized by a single forbidden minor. Inspired by a recent result of Aharoni and Berger, we investigate possible ways to extend the matroid intersection theorem to simplicial complexes.

On Isomorphism of Simplicial Complexes and Their Related Algebras

Saturated simplicial complexes

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...