26,643 research outputs found
The Functor for -cell Complexes and \EHP Sequences
Let be a co--space of -cell complex with all cells in even
dimensions. Then the loop space admits a retract
that is the evaluation of the functor on . In this paper, we
determine the homology and give the \EHP sequence for
the spaces .Comment: 32 page
Chen's double sieve, Goldbach's conjecture and the twin prime problem
We give a more comrehensive treatment of Chen's double sieve and improve
related constants in Goldbach's conjecture and the twin prime problem
Operators on random hypergraphs and random simplicial complexes
Random hypergraphs and random simplicial complexes have potential
applications in computer science and engineering. Various models of random
hypergraphs and random simplicial complexes on n-points have been studied. Let
L be a simplicial complex. In this paper, we study random sub-hypergraphs and
random sub-complexes of L. By considering the minimal complex that a
sub-hypergraph can be embedded in and the maximal complex that can be embedded
in a sub-hypergraph, we define some operators on the space of probability
functions on sub-hypergraphs of L. We study the compositions of these operators
as well as their actions on the space of probability functions. As applications
in computer science, we give algorithms generating large sparse random
hypergraphs and large sparse random simplicial complexes.Comment: 22 page
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