[r-t] Fwd: bobs-only Grandsire Triples

[Alan Reading]

Roy Dyckhoff wrote:
| The novelty is that I reject his argument that there is no touch of
| greater than 5000 changes; I don't claim that there is such a touch, but
| this argument is evidently fallacious.

Presumably his proof that there is no true touch of length exactly 5040
with common bobs only is sound though?
I don't think I've ever seen the proof but it seems highly improbable that
if there was a mistake in that (most important proof) that nobody would
have noticed it by now...
I assume the argument that there is no touch greater than 5000 changes to
which you refer is something that he goes onto?

It would be interesting if you could share the paper mentioned with the
list?

Alan



On 31 January 2017 at 15:11, Philip Earis <pje24 at cantab.net> wrote:

> The following is a message from Roy Dyckhoff, who is having technical
> difficulties sending messages to this list himself.
>
> ==================================
> I have a paper of about 8 pages on Thompson's famous 1886 paper about
> bobs-only Grandsire Triples. It begins with (as background) a short
> proof of his main result, eschewing both group theory and case analysis.
>
> The novelty is that I reject his argument that there is no touch of
> greater than 5000 changes; I don't claim that there is such a touch, but
> his argument is evidently fallacious. Perhaps the search for such a
> touch ceased in 1886; but it seems to me that someone might have another
> look. Modern computers might ease this tedious task.
>
> The crucial point is to consider Q-sets as Q-cycles, and to accept his
> point that if a row in such a cycle is Plained then the next cannot be
> Bobbed. If one sees a touch as determining for each row in a Q-cycle
> whether it is Plained, Bobbed, or Absent, then there is the possibility
> of patterns such as ABPPP, which has no P immediately followed by a B.
> Some of the Q-sets in a long touch will be complete, and so either fully
> Plained or fully Bobbed; but some will include changes not in the touch,
> and here the argument about "all are Plained or all are Bobbed" falls
> down. There is a counterexample of 280 changes to the argument.
>
> Happy to send the paper to those interested.
>
> RD
> University of St Andrews
>
>
>
>
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