
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 nonhomeomorphic _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

