[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"!
RANKIN, RA. "A CAMPANOLOGICAL PROBLEM IN GROUP THEORY." Proceedings of the
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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