The Threshold for Integer Homology in Random d-Complexes

THE THRESHOLD FUNCTION FOR VANISHING OF THE TOP HOMOLOGY GROUP OF RANDOM d-COMPLEXES

For positive integers n and d, and the probability function 0 ≤ p(n) ≤ 1, we let Yn,p,d denote the probability space of all at most d-dimensional simplicial complexes on n vertices, which contain the full (d− 1)-dimensional skeleton, and whose d-simplices appear with probability p(n). In this paper we determine the threshold function for vanishing of the top homology group in Yn,p,d, for all d ...

The threshold for d-collapsibility in random complexes

In this paper we determine the threshold for d-collapsibility in the probabilistic model Xd(n, p) of d-dimensional simplicial complexes. A lower bound for this threshold p = ηd n was established in [?], and here we show that this is indeed the correct threshold. Namely, for every c > ηd, a complex drawn from Xd(n, c n ) is asymptotically almost surely not d-collapsible.

Integral Homology of Random Simplicial Complexes

Generalized Local Homology Modules of Complexes

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...