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Topic: The # Operation
Replies: 2   Last Post: Apr 22, 2005 11:53 AM

 Marc Olschok Posts: 409 Registered: 12/6/04
Re: The # Operation
Posted: Apr 22, 2005 11:53 AM

> "Marc Olschok" <sa796ol@l1-hrz.uni-duisburg.de> wrote in message
> news:3cq077F6p2umuU1@news.dfncis.de...

>> ...
>> For 1 < |U| < 10 there seem to be only models with |U|=4 or |U|=9.
>> However, I have no idea why this is so.

>
> Given that you have not solved the problem, I am amazed that you were able
> to determine that the only values of |U| for which a # operator exists
> within the range 1 < |U| < 10 was 4 and 9. Please post how you were able to
> deduce this.

I threw the specification at mace2 which is part of otter
(see <http://www.mcs.anl.gov/AR/otter/> for more).

Among other things it reported the 4-element model you gave in a
previous posting.

>
> At any rate, this discovery does suggest a conjecture on the possible values
> of |U|. The sequence of possible |U| values starts with
>
> 0, 1, 4, 9, ...
>
> One can easily guess the next number in this sequence.

Certainly. But right now I have no specific idea.
Since x = (xx)(xx) for every x, it might help to investigate
the possible choices for y and z such that x = (xx)(xx) = yz.

Marc