[r-t] Alternating groups in change ringing
strainsteamford0123456789+ringingtheory at gmail.com
Mon Apr 14 15:01:39 UTC 2014
Many years ago I read a paper which I think was called "The Mathematics
of Change Ringing". If I remember correctly, it talked about how sets of
changes form groups under row multiplication (or composition of rows, I
forget the exact terminology). Also, I think there was talk of Cayley
Colour Graphs with changes forming the vertices.
My first question is, does anyone have a copy of this paper that they
could easily email me or give me a link to?
More importantly, I am interested in alternating groups in the context
of change ringing. It is often said that the dihedral group, Dn, is
isomorphic to plain hunt on n bells and that the symmetric group Sn is
isomorphic to the extent on n bells. I've always been interested in the
alternating group, An, which is the group of all even permutations and
would be isomorphic to the set of all in-course changes on n bells. It
occurred to me that the plain course of Stedman Doubles is isomorphic to
the group A5, since Stedman Doubles contains only the place notation 1,3
and 5 which all represent two pairs of bells swapping between any two
rows and hence would preserve the parity of the row.
I was wondering if anyone knew if much had been published on alternating
groups in the context of change ringing? I wanted to do some
investigation into the subject but I don't want to reinvent the wheel if
there is already stuff out there that has been published on the subject!
If anyone could point me in the direction of any literature on the
subject of group theory in change ringing, I would be very grateful.
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