Message #1632

From: djs314djs314 <djs314djs314@yahoo.com>
Subject: Correction of erroneous order-2 Klein’s Quartic permutation count
Date: Sun, 01 May 2011 01:32:29 -0000

Hello all,

Aha! I did make a mistake, as I suspected I might have. It’s been too long since I counted permutations. :) My previous answer was off by a factor of 2; the 2 in the denominator should not have been there. I made the classic mistake of taking even permutations into account when there are identically colored pieces (in this case, stickers). Naturally, with identically colored pieces parity does not matter, as even and odd permutations are identical.

Here is the correct formula and number of permutations:

209!/(((7!)^29)*(6!)) =

2982258374829406765091841007287208110044231115104792401778764352522005836340463837850121874947185190056715803101607827209655156207636181402167465898185982442986345576457227559003601279297679332452494926096129531568368614235884567287678429277548260303941234016334643200000000000000000000

My apologies for not catching this sooner; I’ve been very busy today with emails. I am virtually certain that this count is correct, as I just sent Ray a complete derivation of it (which is how I discovered my error).

Thanks to everyone for your patience, and I’ll keep you informed of my progress.

All the best,
David