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).
I am also constructing an array M_[x,y] comprising black cells and
white cells. The number of black cells in a column is given by
t(n,M_[x,y]). My question is, will it be acceptable in a mathematical
paper
to devise a form of notation referencing an interval [x,y] in such a way
that the values of t(n,M_[x,y]) over [x,y] are precisely those given by
g(n,M_1) for an interval [x,y] in M_1? (i.e. if u divides v, and u is a
member of J, then there is a single black cell on the u-th row and in the
v-th column. Otherwise, there is none such, save in the column indexed by
zero.)
I want to be able to say, 'in this case, the black cells exhibit the
divisibility distribution found for members of J over [x,y], .... and
in this case, they do not'. It strikes me that if it is indeed possible, I
won't need a completely different set of definitions for my array M_[x,y]
as
I have for my matrix M_1.
I was thinking that, for a value of t, the notation would be
t(n,M_[x,y],J). But someone was telling me that this mixture of
arguments is something that is just not done....
With thanks in advance.
|
