Paul,
Many thanks. Comments embedded.
>> 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.
P(m) is a set comprising the first m primes. So if m=3, the members of
P(m)
are 2,3 and 5.
> 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.
I don't know about t by r. The matrix has #J rows, and J is a general
subset
of P(m). It has f columns.
The (i, j) entry of M(x,y)
> is said to be "occupied" if p(i) divides x(j); otherwise, the entry is
> "unoccupied".
Yes.
> *******
>
> 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.
>
Good thinking. I'm much looking forward to any further help.
With Regards.
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