[r-t] Bobs only Stedman Triples

[Andrew Johnson]

> From: edward martin <edward.w.martin at gmail.com>
> Date: 25/06/2012 09:46
> In my very limited experience, strings of 9 consecutive bobs are
> inevitable if looking for 5 or 10 part comps. It is possible to plain
> these out in the basic part but the result will be a round block thus
> to link all parts this string has to be included
If you are talking about B-block based bobs-only magic block composition
then I remember Philip Saddleton saying that there aren't any 5 or 10
part peals.
For the general case, my latest peal disproves this as it just has
5 consecutive bobs (twice), though you could argue it isn't quite on
a 10-part plan as it has the twin bob linkage.

> In Erin Triples you cannot set out the 5040 in mutually exclusive
> bobbed blocks; therefore the hope is to find mutually exclusive,
> equally structured blocks of plain and bobbed sixes.
This is possible - see peals 8,9,10 in the CCCBR collection of
Stedman and Erin Triples.
http://www.ringing.info/stedman.pdf

> If this is achieved then is it possible, within these blocks to
> duplicate Stedman's phenomenon by having a relatively short sequence
> of plain and bobbed six-emds which can contain the same rows but in a
> different sequence? I don't know and don't see how to find out.
I'm not sure on this one, but you can get an arrangement into an odd
number of round blocks. E.g. on a 21-part plan you get a set of
43 round blocks or 79 round blocks. They aren't immediately useful as
some of the blocks are plain courses and some are bob courses.

> Incidentally, I believe that it is not
> possible to obtain a 21-part bobs only of Stedman Triples (This belief
> was instrumental to my investigating why not? and the idea of splicing
> in Erin sixes)
Brian Price proved this in 1953.
http://myweb.tiscali.co.uk/saddleton/stedman/qed.htm
and even allowing multiple round blocks there are no odd numbers of
blocks:
Number of touches dividing into   6 round blocks: 2
Number of touches dividing into  12 round blocks: 15
Number of touches dividing into  14 round blocks: 4
Number of touches dividing into  18 round blocks: 3
Number of touches dividing into  30 round blocks: 2
Number of touches dividing into  40 round blocks: 2
Number of touches dividing into  42 round blocks: 16
Number of touches dividing into  48 round blocks: 19
Number of touches dividing into  54 round blocks: 1
Number of touches dividing into  84 round blocks: 36
Total touches: 100
Search ended at Thu Jun 28 09:28:08 2012
Loop took 0.060000 seconds

Example output:
240!6 3124567QSP--P--*7(3)3426175QS-P--P--PPP--P--P--P--PP----P---P--*7(3)
240!6 3124567QSP--P--*7(3)4236175SQPP--P--P--P--PPP--P--P---P---P----*7(3)


Andrew Johnson

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