pje24 at cantab.net
Sat Aug 5 18:02:00 UTC 2006
Professor Holroyd, you're a genius.
A random question - do any 'perfect' 6-part principle extents of minor exist
(ie a plain course with 120 rows per lead which generates the extent)? I
can't think of anything off the top of my head, but may be missing something
----- Original Message -----
From: "Alexander Holroyd" <holroyd at math.ubc.ca>
To: <ringing-theory at bellringers.net>
Sent: Friday, August 04, 2006 9:30 PM
Subject: Re: [r-t] Crambo
> Are you saying that you can prove it's always possible to get an extent in
> this way from any in-course extent? If so I don't get it. Obviously
> there are lots of ways to resolve the double changes into pairs of single
> changes, but one has to do it in such a way that the 60 out-of-course rows
> so introduced are all different. Most ways fail to achieve this, e.g.
> turning 3.1 into 3220.127.116.11 !
>>> All of them are strange and unsymmetrical, so what is really going one
>>> here? I don't know. E.g. can you prove or disprove that any in-course
>>> extent of doubles can be treated in this way?
>> I wpuld have said yes in that if you have an extent of pure doubles
>> (say Grandsire or Rev Grandsire called P B P B P B or the plain course
>> of Stedman or Rev Stedman or Carter's or Rev Carters) then, since each
>> row is produced by a double then two singles are bound to accomplish
>> the same thing. Thus if we compare the backstroke rows of Crambo we
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