[r-t] Bobs only Erin Triples (was: Composition search)

[Philip Earis]

Alan Burlison:
> 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: 
http://myweb.tiscali.co.uk/saddleton/stedman/bdp.htm

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... 
http://www.bellringers.net/pipermail/ringing-theory_bellringers.net/2012-June/010581.html

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 possible).

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!