50.9 MolienSeries

MolienSeries( psi )
MolienSeries( psi, chi )
MolienSeries( tbl, psi )
MolienSeries( tbl, psi, chi )

returns a record that describes the series [ M_psi,chi(z) = sum_d=0^infty (chi,psi^[d]) z^d ] where psi^{[d]} denotes the symmetrization of psi with the trivial character of the symmetric group S_d (see SymmetricParts).

psi and chi must be characters of the table tbl, the default for chi is the trivial character. If no character table is given, psi and chi must be class function recods.

ValueMolienSeries( series, i )

returns the i-th coefficient of the Molien series series.

    gap> psi:= Irr( CharTable( "A5" ) )[3];
    Character( CharTable( "A5" ),
    [ 3, -1, 0, -E(5)^2-E(5)^3, -E(5)-E(5)^4 ] )
    gap> mol:= MolienSeries( psi );;
    gap> List( [ 1 .. 10 ], i -> ValueMolienSeries( mol, i ) );
    [ 0, 1, 0, 1, 0, 2, 0, 2, 0, 3 ] 

The record returned by MolienSeries has components

summands:

a list of records with components numer, r, and k, describing the summand 'numer' / (1-z^r)^k,

size:

the size component of the character table,

degree:

the degree of psi.

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