Random Abstract Simplicial Complexes Reduction

On Topological Minors in Random Simplicial Complexes

Simplicial Complexes. A (finite abstract) simplicial complex is a finite set system that is closed under taking subsets, i.e., F ⊂ H ∈ X implies F ∈ X. The sets F ∈ X are called faces of X. The dimension of a face F is dim(F ) = |F | − 1. The dimension of X is the maximal dimension of any face. A k-dimensional simplicial complex will also be called a k-complex.

Exponential random simplicial complexes

Abstract Exponential random graph models have attracted significant research attention over the past decades. These models are maximum-entropy ensembles subject to the constraints that the expected values of a set of graph observables are equal to given values. Here we extend these maximum-entropy ensembles to random simplicial complexes, which are more adequate and versatile constructions to m...

On Isomorphism of Simplicial Complexes and Their Related Algebras

Vertex Decomposable Simplicial Complexes Associated to Path Graphs

Introduction Vertex decomposability of a simplicial complex is a combinatorial topological concept which is related to the algebraic properties of the Stanley-Reisner ring of the simplicial complex. This notion was first defined by Provan and Billera in 1980 for k-decomposable pure complexes which is known as vertex decomposable when . Later Bjorner and Wachs extended this concept to non-pure ...

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.