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DPChallenge Forums >> Tips, Tricks, and Q&A >> Interrogation of Art Roflmao
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Showing posts 26 - 43 of 43, (reverse)
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 05/17/2011 10:23:49 AM · #26
WTF did you do with KPriest?!?!?!
 05/17/2011 10:39:26 AM · #27
Ok serious question then,
What is your favourite type of photography and why?
 05/17/2011 11:30:49 AM · #28
Who is Mary?!
 05/17/2011 12:56:50 PM · #29
Thanks so far. Just pm me the questions so he can't see them coming
 05/17/2011 01:12:40 PM · #30
Do you prefer to be surprised with questions, or see them coming?
 05/17/2011 01:47:29 PM · #31
Why pick on Bucky the Wondermule?
 05/17/2011 05:29:26 PM · #32
What should we do about easing the spring?
 05/17/2011 06:09:29 PM · #33
Originally posted by giantmike:
What is the air speed velocity of an unladen swallow?

What do you mean, African or European Swallow?
 05/24/2011 07:31:37 AM · #34
Originally posted by bvy:
Question for you, Art. Let A_n be the alternating group of order n (the group of even permutations on a finite set) with n >= 3. Is it possible to show that any element of A_n can be represented as a three-cycle or a product of three-cycles? Explain.

You're off the hook for this one, Art. Let z be an element of A_n. Since z is an even permutation, it can be expressed as a product of p two-cycles for some positive even integer p:

z = (u1, u2)(u3, u4) â€Â¦ (u[2p-1], u[2p])

As such, we can break this product down sequentially into p/2 pairs. Consider the first pair: (u1, u2)(u3, u4). It either has the form (ab)(cd) or (ab)(ac) where a, b, c and d are unique elements of the permutation set. (If n = 3, then it necessarily takes the last form. Also any pair of the form (ab)(ab) can be eliminated from the product since this is the identity permutation.) (ab)(cd) can be rewritten (adc)(cab), which is a product of three-cycles; (ab)(ac) can be rewritten (acb), which is a three-cycle. Continuing in this manner, the remaining pairs of two-cycles can be replaced with one or two three-cycles, and we arrive at a new product which is a product of three-cycles.

I'll think of another one for you...
 05/24/2011 07:32:56 AM · #35
Originally posted by fldave:
Originally posted by giantmike:
What is the air speed velocity of an unladen swallow?

What do you mean, African or European Swallow?


42.
 05/24/2011 07:59:56 AM · #36
Originally posted by bvy:
Originally posted by bvy:
Question for you, Art. Let A_n be the alternating group of order n (the group of even permutations on a finite set) with n >= 3. Is it possible to show that any element of A_n can be represented as a three-cycle or a product of three-cycles? Explain.

You're off the hook for this one, Art. Let z be an element of A_n. Since z is an even permutation, it can be expressed as a product of p two-cycles for some positive even integer p:

z = (u1, u2)(u3, u4) â€Â¦ (u[2p-1], u[2p])

As such, we can break this product down sequentially into p/2 pairs. Consider the first pair: (u1, u2)(u3, u4). It either has the form (ab)(cd) or (ab)(ac) where a, b, c and d are unique elements of the permutation set. (If n = 3, then it necessarily takes the last form. Also any pair of the form (ab)(ab) can be eliminated from the product since this is the identity permutation.) (ab)(cd) can be rewritten (adc)(cab), which is a product of three-cycles; (ab)(ac) can be rewritten (acb), which is a three-cycle. Continuing in this manner, the remaining pairs of two-cycles can be replaced with one or two three-cycles, and we arrive at a new product which is a product of three-cycles.
(...)


I see
 05/24/2011 08:29:49 AM · #37
What came first: The chicken or the egg?

Not to start a whole debate but if you believe in creation the answer should be Chicken and if you believe in evolution the answer should be the egg.
In creation a "chicken" laid the egg and the egg hatched and it was a "chicken".
In evolution an "almost chicken" (as it was still in the process of evolving) laid an egg and the egg hatched and it was a "chicken" (finished evolving and is a complete chicken as we know it)
 05/24/2011 08:40:42 AM · #38
Originally posted by Silent-Shooter:
What came first: The chicken or the egg?

Not to start a whole debate but if you believe in creation the answer should be Chicken and if you believe in evolution the answer should be the egg.
In creation a "chicken" laid the egg and the egg hatched and it was a "chicken".
In evolution an "almost chicken" (as it was still in the process of evolving) laid an egg and the egg hatched and it was a "chicken" (finished evolving and is a complete chicken as we know it)


Actually, in evolution a dinosaur laid an egg, and out hatched a chicken. ;P
 05/24/2011 09:42:53 AM · #39
Originally posted by Kelli:
Originally posted by Silent-Shooter:
What came first: The chicken or the egg?

Not to start a whole debate but if you believe in creation the answer should be Chicken and if you believe in evolution the answer should be the egg.
In creation a "chicken" laid the egg and the egg hatched and it was a "chicken".
In evolution an "almost chicken" (as it was still in the process of evolving) laid an egg and the egg hatched and it was a "chicken" (finished evolving and is a complete chicken as we know it)


Actually, in evolution a dinosaur laid an egg, and out hatched a chicken. ;P
So the dinosaur was an "almost chicken" then...
 05/24/2011 09:44:47 AM · #40
Originally posted by bvy:
Originally posted by bvy:
Question for you, Art. Let A_n be the alternating group of order n (the group of even permutations on a finite set) with n >= 3. Is it possible to show that any element of A_n can be represented as a three-cycle or a product of three-cycles? Explain.

You're off the hook for this one, Art. Let z be an element of A_n. Since z is an even permutation, it can be expressed as a product of p two-cycles for some positive even integer p:

z = (u1, u2)(u3, u4) â€Â¦ (u[2p-1], u[2p])

As such, we can break this product down sequentially into p/2 pairs. Consider the first pair: (u1, u2)(u3, u4). It either has the form (ab)(cd) or (ab)(ac) where a, b, c and d are unique elements of the permutation set. (If n = 3, then it necessarily takes the last form. Also any pair of the form (ab)(ab) can be eliminated from the product since this is the identity permutation.) (ab)(cd) can be rewritten (adc)(cab), which is a product of three-cycles; (ab)(ac) can be rewritten (acb), which is a three-cycle. Continuing in this manner, the remaining pairs of two-cycles can be replaced with one or two three-cycles, and we arrive at a new product which is a product of three-cycles.

...


I was going to say the exact same thing, just quicker, and prettier.
05/24/2011 11:56:13 AM · #41
When / why did that "burning villages" story start?
 06/04/2011 05:15:58 PM · #42
Did this ever happen ?
 06/04/2011 05:33:45 PM · #43
Don't know. I've since moved on to trying to prove that every Cayley graph is complete.
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