[r-t] Bobs only Erin Triples (was: Composition search)
pje24 at cantab.net
Tue Nov 24 14:12:35 UTC 2015
> Hmm, something conceptually simple but computationally expensive sounds
> more like something I could get my teeth into - thanks!
My pleasure. It is arguably the great unsolved problem in ringing theory,
and deserves fresh attention.
> Have there been any previous attempts at this, and if so, what approach
> did they use? No point reinventing any wheels :-)
Indeed. I think it's fair to say that lots of the previous efforts at
searching for a bobs only extent of Erin triples have been by the great
Stedman triples composers, comparing and contrasting the Erin problem to
the search for a bobs only Stedman triples extent (which was finally
solved in the mid 1990s, after two centuries of work).
For a comprehensive background on bobs only Stedman triples, see this
webpage by Philip Saddleton (often referred to as PABS), which gives a
good historical context:
If you want to see some more recent correspondence linked to Erin, take a
look at the (freely-accessible) archives of this list, eg this thread from
June 2012 which involves Andrew Johnson, PABS, Eddie Martin etc...
In some ways, though, I'd encourage you to approach bobs-only Erin with a
fresh pair of eyes. As you'll see, the links above contain a lot of
Stedman-derived terminology which may be a distraction.
Of course, reinventing the wheel should be avoided. At the most naive
level bobs only Erin triples is still far too huge for a brute force
search...an extent (5040 rows) will consist of 840 divisions of 6 changes
("sixes"), each of which can either be plain (p) or bobbed (b), and 2^840
is unfathomably vast. (Of course, huge pruning of the search space is
In terms of previous searches, both Richard Smith and Iain Anderson (both
on this list), and doubtless others too, have spent time searching for a
bobs only extent of Erin. I think Richard has ruled out a perfect 7-part
composition, and possibly further - I'm sure he'll be able to confirm.
Any progress by anyone on this problem would be awesome!
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