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06/15/2011 11:52:47 PM · #6751 |
I'm all out of ideas.
...hey, I STILL win! I love how that works. |
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06/15/2011 11:58:22 PM · #6752 |
Well, someone needs to work!
Joe....uh........mmm..........ugh! |
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06/16/2011 02:25:28 AM · #6753 |
Oooh! This just in...
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06/16/2011 07:01:01 AM · #6754 |
i dont know who sent you that but they were misinformed
gene rayburn? wow the ghost of games shows past. |
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06/16/2011 10:11:05 AM · #6755 |
I saw him on TV a time or two. Totally unreliable!!! That is SO not real!
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06/16/2011 10:41:54 AM · #6756 |
| geez!!!! I win so you can all just....shhhhhoeeee |
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06/16/2011 11:25:23 AM · #6757 |
Originally posted by bvy:
You all are probably wondering if all Cayley graphs are regular. It turns out they're 2|S|-regular (|S| being the order of the generating set S, of course). Proof to follow... |
As promised...
Cay(S:G) is regular; the degree of each vertex is 2|S|:
Let x be a vertex of Cay(S:G). Then there are arcs from x to xs for each s in S. Hence the outdegree of x is |S|. Similarly, given a vertex x, we must show that for each s in S there is a corresponding vertex y in Cay(S:G) such that ys = x. Closure on the underlying group guarantees this, and the indegree of x is also |S|. Hence the total degree of x is 2|S| and Cay(S:G) is 2|S|-regular. |
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06/16/2011 12:25:12 PM · #6758 |
| Di-dit, Di-dah-dah Dah-dah-dah Dah-dit, Dah Di-di-di-dit Dit, Dah Di-di-di-dit Di-dah-dit Dit Di-dah Dah-di-dit |
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06/16/2011 12:31:51 PM · #6759 |
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06/16/2011 12:47:24 PM · #6760 |
| I am not sure that is mumbling. I think it might be Morse code. |
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06/16/2011 01:02:01 PM · #6761 |
| probably to the tune of "I win...I win...I win" |
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06/16/2011 01:08:13 PM · #6762 |
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06/16/2011 01:12:33 PM · #6763 |
| seriously did you not read my post...end of story...done..."I win" |
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06/16/2011 01:44:48 PM · #6764 |
| I'm winning as I leave town... |
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06/16/2011 02:17:21 PM · #6765 |
| Good! This town wasn't big enough for both of us. :P |
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06/16/2011 04:45:32 PM · #6766 |
whooeee ooooeeee oooooooooo. wah wah wah.
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06/16/2011 05:22:48 PM · #6767 |
| Hurtin' music aint getting you nowhere. |
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06/16/2011 05:42:48 PM · #6768 |
| I aint goin nowhere. I'ma staying right here. Winning. |
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06/16/2011 05:53:20 PM · #6769 |
Sir, I am going to have to confiscate those fire arms... No need for violence... Just hand em over and walk away.. |
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06/16/2011 06:09:41 PM · #6770 |
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06/16/2011 06:16:35 PM · #6771 |
BRING IT ON SUCKAS!!!!
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06/16/2011 06:35:36 PM · #6772 |
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06/16/2011 06:41:34 PM · #6773 |
| Bribery... It's a wonderful thing! I win ;) |
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06/16/2011 06:44:02 PM · #6774 |
Um, not until I get paid. :P
eta: ...oh, I just now saw that. Still not enough. :P
Message edited by author 2011-06-16 18:44:49. |
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06/16/2011 06:45:39 PM · #6775 |
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