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

 Messages: [ Previous | Next ]
 David C. Ullrich Posts: 21,553 Registered: 12/6/04
Re: Stone Cech
Posted: Mar 23, 2013 1:48 PM

On Fri, 22 Mar 2013 20:27:15 -0700 (PDT), Butch Malahide
<fred.galvin@gmail.com> wrote:

>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
>>
>> 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.

No, this is not something you should take my word for! Sounds
like you know more about such things than I do - I was just
conjecturing it was "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?

I certainly don't know. My wild-ass guess is maybe. Seems like
this question is more likely than the other of being susceptible
to some clever idea, although I have no idea what that idea might be,
not being all that clever.

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