Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Stone Cech
Replies: 49   Last Post: Mar 28, 2013 12:15 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Stone Cech
Posted: Mar 22, 2013 11:27 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Mar 22, 10:52 am, David C. Ullrich <ullr...@math.okstate.edu>
wrote:
> I just realized I have no idea whatever how to write
> a correct algorithm here, even without worrying
> about efficiency.
>
> An equivalence relation on the 2n endpoints
> determines a compactification. It also determines
> a graph, where the vertices are the equivalence
> classes of endpoints and the edges are the
> original segments. Earlier, thinking that I was
> thinking about deciding when two of these
> compactifications are homeomorphic, I was
> actually thinking about how to determine
> whether two of the graphs are isomorphic.
> That's a strictly weaker condition... I have
> no idea how I'd check whether two equivalences
> gave homeomorphic compactifications.


You mean, non-isomorphic is a weaker condition than non-homeomorphic.

The remedy for that is to stick to graphs with no vertices of degree
2. (OK, you have to make an exception for the graph consisting of a
single vertex of degree 2, corresponding to the one-point
compactification of R.)

All right, the problem is to determine the number of nonisomorphic
pseudographs (undirected graphs which may have loops and multiple
edges) with p vertices and q edges, and with no vertices of degree 2.
(Alternatively, determine the number of nonisomorphic *connected*
pseudographs with p vertices, q edges, and no vertices of degree 2.)
Since we are counting isomorphism types, it's a problem for Burnside-
Polya-Redfield enumeration theory. Which I'm not well enough
acquainted with to know the difference between a merely difficult
problem and an impossible problem, so I have to take your word for it
that it's impossible.

All right, but what about the order-of-magnitude or asymptotic
problem, which was also implicit in my open-ended "how many" question?
Does f(n)^(1/n) approach a limit? Is that also hopeless?


Date Subject Author
3/14/13
Read Stone Cech
William Elliot
3/14/13
Read Re: Stone Cech
fom
3/15/13
Read Re: Stone Cech
fom
3/16/13
Read Re: Stone Cech
William Elliot
3/15/13
Read Re: Stone Cech
David C. Ullrich
3/17/13
Read Re: Stone Cech
William Elliot
3/17/13
Read Re: Stone Cech
David C. Ullrich
3/17/13
Read Re: Stone Cech
fom
3/18/13
Read Re: Stone Cech
David C. Ullrich
3/18/13
Read Re: Stone Cech
fom
3/18/13
Read Re: Stone Cech
David Hartley
3/19/13
Read Re: Stone Cech
William Elliot
3/19/13
Read Re: Stone Cech
David Hartley
3/19/13
Read Stone Cech
William Elliot
3/20/13
Read Re: Stone Cech
Butch Malahide
3/20/13
Read Re: Stone Cech
David C. Ullrich
3/20/13
Read Re: Stone Cech
Butch Malahide
3/20/13
Read Re: Stone Cech
Butch Malahide
3/21/13
Read Re: Stone Cech
quasi
3/21/13
Read Re: Stone Cech
quasi
3/21/13
Read Re: Stone Cech
quasi
3/21/13
Read Re: Stone Cech
quasi
3/21/13
Read Re: Stone Cech
Butch Malahide
3/21/13
Read Re: Stone Cech
quasi
3/22/13
Read Re: Stone Cech
Butch Malahide
3/22/13
Read Re: Stone Cech
Butch Malahide
3/22/13
Read Re: Stone Cech
Butch Malahide
3/22/13
Read Re: Stone Cech
quasi
3/22/13
Read Re: Stone Cech
David C. Ullrich
3/22/13
Read Re: Stone Cech
David C. Ullrich
3/22/13
Read Re: Stone Cech
Butch Malahide
3/23/13
Read Re: Stone Cech
Butch Malahide
3/23/13
Read Re: Stone Cech
David C. Ullrich
3/23/13
Read Re: Stone Cech
David C. Ullrich
3/23/13
Read Re: Stone Cech
Frederick Williams
3/23/13
Read Re: Stone Cech
David C. Ullrich
3/23/13
Read Re: Stone Cech
Frederick Williams
3/22/13
Read Re: Stone Cech
Butch Malahide
3/23/13
Read Re: Stone Cech
David C. Ullrich
3/22/13
Read Re: Stone Cech
Butch Malahide
3/23/13
Read Re: Stone Cech
quasi
3/23/13
Read Re: Stone Cech
Butch Malahide
3/23/13
Read Re: Stone Cech
Butch Malahide
3/24/13
Read Re: Stone Cech
quasi
3/24/13
Read Re: Stone Cech
Frederick Williams
3/24/13
Read Re: Stone Cech
quasi
3/25/13
Read Re: Stone Cech
Frederick Williams
3/28/13
Read Re: Stone Cech
Frederick Williams
3/25/13
Read Re: Stone Cech
quasi
3/19/13
Read Re: Stone Cech
David C. Ullrich

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.