I wrote:
> Since F is rank 0, then W must be a prefix of L, hence W -: 2 {. L .
And
> since #6 1 5 2 3 4 is 6, then w1=l1=6 .
Ah, this morning I realized I misread your message; I thought you had given
the ranks, not shapes, of your inputs. So the above was mistaken as were
some of my other comments. Sorry about that.
Moving forward, with only the information you've given us, I think Raul's
analysis:
> (l1 F w1) > l1 F w2
> (l1 F w2) >: l2 F w1
> (l2 F w1) > l2 F w2
> (l2 F w2) >: l3 F w1
> (l3 F w1) >: l3 F w2
is about the best you can get (and it's pretty easy to use J tools to
convince yourself it is correct -- remember \: is a stable sort).
Using these relationships, if you make some assumptions about the values,
then you could infer some of the properties of F, and vice versa. Of course
you're still stuck with an infinite number of candidates for either, but at
least they'd all be in the same "family".
We're all very curious. Can you give some more background on this problem?
Where did it come from? What is its context? Why do you know the shapes of
the input, some properties of F, and the grade vector of the raveled output,
but nothing else? The more relevant information we have, the tighter we can
make the solution.
-Dan
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