Comments on: Olivier Messiaen & Mathieu 12

By: Thane Plambeck

Thane Plambeck — Mon, 08 Mar 2010 03:33:10 +0000

People might like “Topsy Turvy,” Oskar van van Deventer’s mechanical implementation of Mathieu M12

http://www.youtube.com/watch?v=H8ZcYvU0sLY

By: John McKay

John McKay — Sun, 03 Jan 2010 04:10:11 +0000

Some recent incarnations of Mathieu groups are found in a paper by Conway, McKay & Trojan in Proc AMS Jan 2010.

[This contains a fulfilled footnote not in the arxiv.org version.]

Gal(x^24+x+t)/F2(t) = M24 for instance. How about all ten Mathieu groups? Do they too have nice polynomials in their natural characteristic?

By: Pieter Belmans

Pieter Belmans — Fri, 01 Jan 2010 13:50:26 +0000

Given that $[S12:M12]$ is 5040 it might imply "quite low". This is far from conclusive, as you'd need generating permutations, but I think it shows it is at least unlikely.

What's more interesting is the choice of his original series: from a strictly serial/atonal viewpoint it is quite bad I could say. It contains a certain structure and notes [7-10] clearly indicate a d minor key with a I-VII progression. So I guess, given the hint of improbability and the original series being not so interesting, series-theoretically speaking, the permutations are deliberatly chosen.

But I could be very wrong.

By: Norbert Dufourcq

Norbert Dufourcq — Thu, 31 Dec 2009 17:21:04 +0000

What are the odds for two randomly chosen permutations in S12 to generate an M12? (Sorry if this is a trivial question; I'm totally ignorant here.)

By: Isar

Isar — Thu, 31 Dec 2009 15:15:04 +0000

After the comments on your Bourbaki posts, I was already hoping that you would be intrigued enough by Messiaen & Maths to write a post or two on that topic too... Great to see this wish come true!

(Let's hope that some more of our wishes will come true in 2010. All the best, and see you soon...)