The Redfield operators

#### 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

 The Redfield operators