#### The Redfield operators

Redfield defined in his article [16] two linear operators, the so called
cup and cap operator *Ç*. His theory turned out to be a generalisation of
Pólyas
theory.
Many years later Read rediscovered these operators as *N{.*.} *
operators [14][15].
These operators act on a finite sequence of cycle indices.
The result of the cup operator is again a polynomial in several
indeterminates, the result of the cap operator is just the sum of the
coefficients of the result of the cup operator.
In SYMMETRICA there are the two routines

INT redf_cup(a,b) OP a,b;
INT redf_cap(a,b) OP a,b;

In both cases `a`

is a VECTOR object, and each entry of `a`

is a
polynomial. `b`

is either the cup or cap product of these polynomials.
The main computation in these routines is done by
static INT redf_formel(a,n,b) OP a,b; INT n;

where `a`

is a VECTOR object, which holds the information about
the cycle type of the permutations, `b`

is the result (an INTEGER
object). The corresponding operator is acting on `n`

*+1* cycle
indices.

harald.fripertinger@kfunigraz.ac.at,

last changed: November 19, 2001