[r-t] ringing the Mathieu group

Alexander Holroyd holroyd at math.ubc.ca
Wed Apr 27 00:19:19 UTC 2011

In a similar vein, does anyone know how to get an in-course extent of 
caters using only the place notations 1, 5, and 9?

On Tue, 26 Apr 2011, Alexander Holroyd wrote:

> Here is today's brain teaser.
> Consider the three 12-bell place notations
> x 125T 18ET
> The group generated by these pns (i.e. the set of all rows you can get to 
> from rounds using only these pns) contains 95040 rows.  It is a very 
> interesting group from a mathematical perspective, called the Mathieu Group 
> M_12.  (It is the second smallest of the 26 "sporadic groups").  One 
> interesting property is that it is "sharply 5-transitive", which means that 
> any given 5 bells (e.g. 12345) ring exactly once of each of the possible 
> places that 5 bells can occupy (counting different orders of 12345 as 
> different), giving 12x11x10x9x8 = 95040 rows.
> According to the "Lovasz conjecture", it should be possible to ring a true 
> round block of these 95040 rows using only these three pns.  Can anyone come 
> up with an elegant way of doing this?  It would obviously be nice to do it 
> right-place, ie without 3 consecutive blows.  I don't know whether that's 
> possible.
> Ander

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