Message #3352

From: joelkarlsson97@gmail.com
Subject: Re: About the number of permutations of MC4D calculating
Date: Sat, 07 May 2016 01:52:34 -0700

I think it’s time to revive this old thread since I have found that there is a difference between the value of the number of configurations of the 5^4 calculated by David Smith (in his n^4 paper) and the one calculated by Eric Balandraud (at Superliminal). I have tested applying Smith’s formula and this gives the same value as Smith derives earlier in his paper. They differ by a factor of 1.5 (Smith’s value is the greater one) and I think that Balandraud might have missed something or simply mistyped the calculation. What do you think?

Balandraud’s calculation (which gives the value at Superliminal):
48!/(6!)^8 * 96!/(12!)^8 * 64!/(8!)^8 * (24!*32!)/2 * 3!^31 * 2^23 * 64!/2 * 3^63 * 16! *(4!/2)^15 * 4 * 96!/(4!)^24 * 2^95 * 96!/(4!)^24 * 2^95

Smith’s calculation (which corresponds to Smith’s formula):
(16!/2) * (24!*32!/2) * 64!/2 * (96!/24^24)^2 * 64!/(8!)^8 * 96!/(12!)^8 * 48!/(6!)^8 * 12^16/3 * 6^32/2 * 3^64/3 * 2^24/2 * (2^96/2)^2

It’s also worth mentioning that Smith’s formula and Balandraud’s calculations provide the same value for the 3^4 and 4^4 cube.