Dave Matthews wrote:

> Andrew the Orchid wrote:
> 
> 
>> Well, one of us has fluffed up somewhere :-S Since the procedure you 
>> undertook is simpler, I suspect it was me :-$
>>
>> Andrew.
> 
> 
> Well, again studiously avoiding doing anything resembling mathematics 
> myself, I downloaded a "KnotTheory" Mathematica package ( 
> http://www.math.toronto.edu/~drorbn/KAtlas/Manual/index.html ), and 
> typed in Jones[TorusKnot[3,2]][q], which produced q + q^3 - q^4 (which 
> is the same as for one of the Trefoil knots, and the picture the package 
> gives for the (3,2) Torus knot looks like a trefoil.  See the 
> attachment.  If I recall correctly (and that's a big ^if^), the 
> exponents in the Jones polynomial should always work out to be positive 
> or negative integers.  I suppose now I'm going to have to sit down and 
> think it through again.  I'm too old for this ;-)
> 
> Dave Matthews
> 
> ------------------------------------------------------------------------
> 
Now I notice that the handed-ness is reversed (he said, replying to 
himself.)  I see why:  I actually had to scale my earlier image by -1 to 
get Mike Williams' knot, and then also scaled the trefoil.  So I guess 
we should get q^-1 + q^-3 - q^-4 for the Jones polynomial of either or both.

Dave Matthews

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