On Topological Minors in Random Simplicial Complexes

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 ...

Se p 20 07 Algebraic Shifting and f - Vector Theory Thesis submitted

This manuscript focusses on algebraic shifting and its applications to f -vector theory of simplicial complexes and more general graded posets. It includes attempts to use algebraic shifting for solving the g-conjecture for simplicial spheres, which is considered by many as the main open problem in f -vector theory. While this goal has not been achieved, related results of independent interest ...

Algebraic Shifting and f-Vector Theory

This manuscript focusses on algebraic shifting and its applications to f -vector theory of simplicial complexes and more general graded posets. It includes attempts to use algebraic shifting for solving the g-conjecture for simplicial spheres, which is considered by many as the main open problem in f -vector theory. While this goal has not been achieved, related results of independent interest ...

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.

On Isomorphism of Simplicial Complexes and Their Related Algebras