Non Total-Unimodularity Neutralized 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 ...

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}...

On Isomorphism of Simplicial Complexes and Their Related Algebras

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 Fredholm determinants in topology

For a finite simple graph G with adjacency matrix A, the Fredholm determinant ζ(G) = det(1 + A) is 1/ζG(−1) for the Bowen-Lanford zeta function ζG(z) = det(1 − zA)−1 of the graph. The connection graph G’ of G is a new graph which has as vertices the set V ′ of all complete subgraphs of G and where two such complete subgraphs are connected, if they have a non-empty intersection. More generally, ...