A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of a given symmetry type and forms from them symmetrized products of a given degree and other symmetry type . A plethysm
(1)
|
satisfies the rules
(2)
|
(3)
|
(4)
|
(5)
|
where is the coefficient of in ,
(6)
|
where is the partition of conjugate to , and
(7)
|
where is the coefficient of in the inner product (Wybourne 1970).