Plethysm
A group theoretic operation which is useful in the study of complex atomic spectra. A plethysm takes a set of functions of agiven symmetry type 
and forms from them symmetrized products of a given degree 
and other symmetry type 
.A plethysm
satisfies the rules
where
is the coefficient of 
in 
,
where
is the partition of conjugate to , and
where
is the coefficient of in the inner product 
(Wybourne 1970).
References
Littlewood, D. E. ``Polynomial Concomitants and Invariant Matrices.'' J. London Math. Soc. 11, 49-55, 1936. Wybourne, B. G. ``The Plethysm of 
-Functions'' and ``Plethysm and Restricted Groups.'' Chs. 6-7 in Symmetry Principles and Atomic Spectroscopy. New York: Wiley, pp. 49-68, 1970.
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