The Redfield operators
Redfield defined in his article [16] two linear operators, the so called
cup and cap operator ∩ . 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 "at" uni-graz.at, May 26,
2011
