Collapsibility of Simplicial Complexes of Hypergraphs

Collapsibility and Vanishing of Top Homology in Random Simplicial Complexes

Let ∆n−1 denote the (n − 1)-dimensional simplex. Let Y be a random d-dimensional subcomplex of ∆n−1 obtained by starting with the full (d − 1)-dimensional skeleton of ∆n−1 and then adding each d-simplex independently with probability p = c n . We compute an explicit constant γd, with γ2 ' 2.45, γ3 ' 3.5 and γd = Θ(log d) as d → ∞, so that for c < γd such a random simplicial complex either colla...

On Isomorphism of Simplicial Complexes and Their Related Algebras

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.

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}...

synthesis of binuclear platinum complexes containing biphosphine ligand

هدف از این مطالعه طراحی یک روش کلی برای سنتز یک سری از کمپلکس های دو هسته ای متقارن سیکلومتاله شده پلاتین (ii) بوده که دارای یک لیگاند پل زن(1,2-bis[bis(pentafluoro-phenyl)phosphino]ethane),dfppe, است. از واکنش cis-[pt(r)2(sme2)2]، که در آنr= para-tolyl ، با یک اکی والان از لیگاند benzo[h]quinoline,bhq، در استون محصول [pt(r)(bhq)(sme2)] که در آن r= para-tolyl بدست می آید. همچنین از واکنش 5/0 اک...