In article <CSYSj.7785$6a2.3172@[EMAIL PROTECTED]
>, Jack <jj@[EMAIL PROTECTED]
>
wrote:
> I'm wondering if there is anything especially problematic about the
wording
> of the questions I have posed on this newsgroup. I re-write one of them,
> below, hoping this time it's all fully clear:
>
> Take x and y to be integers.
> If we have a set P(m) comprising the first m primes and a
> general subset J of of P(m), then I am constructing a matrix M_1 in
> which the members of J index the rows. Let the columns number f. Let p
be a
> member of J. The matrix components, of which in any subinterval [x,y] of
> [0,f-1], there are (y-x+1)*J, are either occupied or unoccupied. If n is
an
> integer indexing a column, the occupied matrix components are given by
> (p|n), save for zero which contains #J occupied matrix components. The
> number of occupied matrix components in the n-th column is given by
> g(n,M_1).
Let's see if I understand all this. I'll start over.
*****
Let P(m) be the m-th prime and let p(1) < p(2) < ... < p(t) <= P(m) be
primes.
Let f be an integer and let 1 <= x(1) < x(2) < ... x(r) <= f be
integers and let M(x,y) be a t by r matrix. The (i, j) entry of M(x,y)
is said to be "occupied" if p(i) divides x(j); otherwise, the entry is
"unoccupied".
*******
I don't know where all of this is heading but, if you can, I'd
recommend that "occupied" entries have value 1 and "unoccupied" entries
have value 0. Then your g(n, M_1) is just the sum of the entries in the
n-th column.
I'll stop until I'm sure we are on the same page so far.
[...]
--
Paul Sperry
Columbia, SC (USA)
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