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

 Messages: [ Previous | Next ]
 Butch Malahide Posts: 894 Registered: 6/29/05
Re: Stone Cech
Posted: Mar 23, 2013 11:58 PM

On Mar 23, 8:54 pm, Butch Malahide <fred.gal...@gmail.com> wrote:
> On Mar 23, 5:25 pm, quasi <qu...@null.set> wrote:
>

> > Butch Malahide wrote:
>
> > >Now I get 2, 7, 21, 61, 180 for the first five values. Doesn't
> > >match anything in the OEIS. I did the work slowly and carefully
> > >(took about an hour and a half), and so I'm reasonably sure my
> > >numbers are correct.

>
> > I wrote a program to do the counts.
>
> > It's very slow (it was designed for ease of programming, not for
> > speed of execution), but at least it's automatic.

>
> > For n = 1, 2, 3, 4, 5, I get the counts
>
> >    2, 7, 21, 61, 178
>
> > so I match your counts until n = 5.
>
> > To help identify the cause of the discrepancy, let me ask this:
>
> > For n = 5 (5 segments) how many non-homeomorphic _connected_
> > compactifications did you get which cannot be represented with
> > less than 5 segments? I get 39 such spaces.

>
> Last night I counted 41 of them. I'll count them again and let you
> know how many I get this time.

Evidently, I didn't count them carefully enough last night. Now I get
39 connected graphs, making a total of 178. I was wrong, you were
right. Nice program you have there. In case anyone wants to see my
work, here are the 39 connected pseudographs with 5 edges and no
vertices of degree 2. Each pseudograph is described (incompletely) by
giving its degree sequence and, after a semicolon, the number of
loops.

10;5

9,1;4
7,3;2
7,3;4
6,4;1
6,4;3
5,5;0
5,5;2
5,5;4

8,1,1;3
6,3,1;1
6,3,1;2
6,3,1;3
5,4,1;0
5,4,1;1
5,4,1;2
5,4,2;3
4,3,3;0
4,3,3;1
4,3,3;1
4,3,3;2
4,3,3;3

7,1,1,1;2
5,3,1,1;0
5,3,1,1;1
5,3,1,1;2
5,3,1,1;2
4,4,1,1;0
4,4,1,1;1
4,4,1,1;2
3,3,3,1;0
3,3,3,1;1
3,3,3,1;2

6,1,1,1,1;1
4,3,1,1,1;0
4,3,1,1,1;1
4,3,1,1,1;1

5,1,1,1,1,1;0
3,3,1,1,1,1;0

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