[r-t] Grandsire Minor

Alexander Holroyd holroyd at math.ubc.ca
Sun Feb 17 22:14:00 UTC 2013

On Sun, 17 Feb 2013, Richard Pullin wrote:

> On a similar wavelength, I'd be interested to know if anybody has ever
> come up with a 5040 of Grandsire Triples made up of five unjoinable
> bobs-only blocks. Or perhaps as the Q-sets are wholly In-Course in
> Triples, the anti bobs-only law doesn't allow events to get this
> 'near' to a bobs-only extent, unlike in Minor where the feature of the
> Q-set altering the nature of the rows can cause the added obstacle of
> needing to arrive in the blocks 'in the right direction'.

That isn't possible.  Any partition of the extent into mutually true 
in-course blocks of Grandsire Triples has an even number of blocks.  This 
was proved by W H Thompson in 1880 or so.  Professional mathematicians 
caught up with ringers in 1948 when Rankin published a formal proof of 
this and its natural generalizations.  This proof was simplified by Swan 
in 1999.

I guess this is what you are referring to as "the anti bobs-only law"!

Cambridge Philosophical Society. Vol. 44. 1948.

Swan, Richard G. "A simple proof of Rankin's campanological theorem." The 
American mathematical monthly 106.2 (1999): 159-161.

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