[r-t] Fwd: bobs-only Grandsire Triples
holroyd at math.ubc.ca
Fri Feb 3 01:33:05 UTC 2017
This looks like a nice write up, but I would say that the "modern" way to
establish the non-existence of a bobs-only extent is simply that it is an
immediate special case of Rankin's theorem (of which Swan's is the "book
proof"). Of course, Thompson still gets full credit for the first proof.
Rankin's and Swan's can be seen as generalizations that closely follow
I thought Thompson was the senior wrangler at Cambridge? That wouldn't
square too well with the assertion that he was "not a mathematician".
Also, I'm not sure it is accurate to say that Thompson was "not aware of
group theoretic tools". The fact that he proved an interesting result in
group theory seems to strongly suggest the opposite! Remember that
abstract combinatorial group theory as we know it today was barely around
at that time.
By the way, understanding the Thomson/Rankin obstruction was the
key step in my paper on "Snake in the Box codes" which solved a minor open
problem arising in flash memory design.
On Wed, 1 Feb 2017, Martin Bright wrote:
> A student here in Leiden wrote a nice undergraduate thesis on this
> topic with me last year. He also noticed that the argument about the
> maximum length of a bobs-only touch doesn't work, and came up with a
> new argument along similar lines.
> Apart from anything else, his thesis is a very nice modern
> presentation of Thompson's proof in mathematical language. It's in
> English and available here:
> Martin Bright
> On 31 January 2017 at 17:21, Roy Dyckhoff <roy.dyckhoff at googlemail.com> wrote:
>> On 31/01/2017 16:08, Alan Reading wrote:
>> 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 believe that his main proof (about extents) is essentially correct.
>> I assume the argument that there is no touch greater than 5000 changes to
>> which you refer is something that he goes onto?
>> Just so.
>> It would be interesting if you could share the paper mentioned with the
>> Now done.
>> See https://dl.dropboxusercontent.com/u/9941616/Bobs-onlyGT.pdf
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