Re: Four-author theorem?

On Nov 12, 10:45 am, valeos...@xxxxxxxxxxxxxxxxxxxxxx (Miika) wrote:
 Jof  wrote:
Will Murray mentioned something about the "four-author theorem" in the
thread about Lisa Simpson juggling, but I can't find any reference to it and
would like to hear a bit more about it. Can anyone help me?

Here's what he wrote in that thread:

Will Murray wrote:
In 2006 I juggled and gave a lecture on siteswap math for a group of
Simpsons and Futurama writers and producers. Groening wasn't there,
but David Cohen and George Meyer were. I opened by showing how
siteswap explains the difference between the cascade and the shower
pattern that you see in many cartoons of juggling. From there we went
on to prove the four-author theorem counting the number of patterns.
A lot of the people there had scientific backgrounds -- Cohen in
particular clearly followed the whole thing and asked some good
questions.

 He's referring tohttp://www.math.ucsd.edu/~fan/ron/papers/94_01_juggling.pdf
which appeared in American Mathematical Monthly in 1994, and the theorem
counts the number of siteswaps of given length and number of balls.

 Anyone want to figure out an analogous formula for given length and
maximum allowed throw?

-Miika

--

(btw, tämä on sadaskuudeskymmenesneljäs viestini tässä uutisryhmässä.)

--
----== posted viawww.jugglingdb.com==----

Indeed, that's what I meant, Theorem 3 in that paper. With period n
and fewer than b balls, there are exactly b^n patterns. The proof
given in the paper is pretty tricky, but as the authors mention, there
are other combinatorial proofs that can be easily presented to a lay
audience. Thanks, Miika!

Will

PS. Coincidentally, I saw one of the four authors Emman suggested --
Mike Day -- juggling at the Nomadic Festival this past weekend. He
was having fun with six and seven balls!
.

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