Gene's Improved notation for prime-form reduction

Carl, See 8118: (quoting Gene)

It seems to me that the set of prime-form reductions of n things
taken m at a time modulo some permutation group of degree G could be
given a name--"(n,m) reduced G" or "G{n,m}" or something--and then
we'd really be cooking. The prime form in question could be defined
as the least base-2 number in the orbit. You might also want a name
for the function which takes a chord or PC or whatever you wish to
call it to its G-reduction. Something like "Pfred(s, G)" where s is
the PC set and G is the permuation group.

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@u...> wrote:
> Carl, See 8118: (quoting Gene)
>
> It seems to me that the set of prime-form reductions of n things
> taken m at a time modulo some permutation group of degree G could be
> given a name--"(n,m) reduced G" or "G{n,m}" or something--and then
> we'd really be cooking. The prime form in question could be defined
> as the least base-2 number in the orbit. You might also want a name
> for the function which takes a chord or PC or whatever you wish to
> call it to its G-reduction. Something like "Pfred(s, G)" where s is
> the PC set and G is the permuation group.

I just realized that I am not completely sure he was talking about a
reduction down to interval vector count - but one could use this
notation anyway. (I think he is talking about reduction to, for
example, C4 X S3 or any of a number of permutation groups)

>Carl, See 8118: (quoting Gene)
>
>It seems to me that the set of prime-form reductions of n things
>taken m at a time modulo some permutation group of degree G could be
>given a name--"(n,m) reduced G" or "G{n,m}" or something--and then
>we'd really be cooking. The prime form in question could be defined
>as the least base-2 number in the orbit. You might also want a name
>for the function which takes a chord or PC or whatever you wish to
>call it to its G-reduction. Something like "Pfred(s, G)" where s is
>the PC set and G is the permuation group.

Thanks!

-C.