In article <f_rTj.9452$NZ7.1062@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
[...]
> > I don't think we know what a _general_ subset is.
> >
>
> I had thought it was like a proper subset except that the members could
be
> exactly the same as the set itself. So if J is a general subset of P(m),
it
> may (or may not) be the same as P(m). That, at least, is how I wanted to
> define J.
Just plain "subset" would do. If you want to emphasize that equality is
allowed you can add the phrase "not necessarily proper" but that is
really not essential.
[...]
As near as I can tell, it boils down to this:
Let J be a sequence of primes p(1) < p(2) < ... < p(t);
Let C be a sequence of integers x(1) < x(2) < ... < x(r).
Define M(J,C) to be the t x r matrix whose (i,j) entry is 1 if p(i)
divides x(j) and is 0 otherwise.
For example let J be 2, 5, 11 let C be 4, 15, 16, 22 then M(J,C) is
1 0 1 1
0 1 0 0
0 0 0 1.
If this is really what you intended, you might want to rewrite the rest
of it in this sprit.
I forgot to mention that a binary matrix is the adjacency matrix for a
simple non-directed graph. That is, your whole setup could be in terms
of graphs instead of matrices. A quick look at Wikipedia might tell you
if that would be of any use to you.
Incidentally, the matrix multiplication (1, 1, ..., 1)*M(J,C) will give
you, all at once, the number of non-zero entries in each column of
M(J,C).
--
Paul Sperry
Columbia, SC (USA)
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