[r-t] ringing-theory Digest, Vol 190, Issue 8

[Robert Bennett]

Peter Scott's example seems to come round after 1 lead.
Since rounds is part of all the different cycles, it is not fair to say
that it belongs to the plain bob cycle.
This is like saying that any number is divisible by 1.

I think that there are 24 possible leads for single hunt minor methods,
which belong to 6 cycles.
One of these, 34562, 45623, 56234 and 62345 cannot be reached by a
symmetrical non-jumping method.
Apart from the plain bob sets, the other 4 sets are :
35642,54263,46325,62534;
64235,52643,36524,45362;
42563,54632,65324,36245;
34625,46532,65243,52364.

There are  6 possible leads for doubles methods (3524, 4253, 3452, 5234,
4532, 5423) so presumably there are
120 leads for triples methods and 720 for major methods, but some of these
cannot be reached from symmetrical methods.

A complication that applies to doubles and triples etc is that there can be
either two pivot bells or none.
 Some leads can be reached using one system but not the other (I think).

Robert Bennett

Robert Bennett


On Sun, Feb 21, 2021 at 12:00 AM <ringing-theory-request at bellringers.org>
wrote:

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>    1. Re: Plain Bob leadheads with 14 le (PeterScott)
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> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 19 Feb 2021 21:44:19 +0000
> From: PeterScott <peter at homescott.free-online.co.uk>
> To: ringing-theory at bellringers.org
> Subject: Re: [r-t] Plain Bob leadheads with 14 le
> Message-ID:
>         <cfa40de99b34f064f0cff9db5176d096 at homescott.free-online.co.uk>
> Content-Type: text/plain; charset=US-ASCII; format=flowed
>
> "Please can someone produce, or point me at, a concise proof of this
> lemma:
> PB1: In a palindromic treble-dominated method with Plain Bob leadheads,
> on an even number of bells, the lead end place notations must be 12 or
> 1n.
> "
>
> Proposition: in Minor there are five "Plain Bob Leadheads", one for each
> of the working bells.
> (Is anyone going to dispute that ?? OK read on:)
>
> By counterexample to the lemma, consider this minor method: (palindromic
> treble-dominated method with Plain Bob leadheads)
>
> 3456.1456.1256.1236.1234 hl=36 le=14
>
> The method extends in the obvious manner to 8, 10, 12, ...
>
> :-)
> Regards
> PeterScott
> Sheffield
>
>
>
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> End of ringing-theory Digest, Vol 190, Issue 8
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