Plethysm

In algebra, plethysm is an operation on symmetric functions introduced by Littlewood (1936, p. 52, 1944, p.329), who denoted it by {λ}⊗{μ}. The word "plethysm" for this operation (after the Greek word πληθυσμός meaning "multiplication") was introduced later by Littlewood (1950, p.289, 1950b, p.274), who said that the name was suggested by M. L. Clark.

If symmetric functions are identified with operations in lambda rings, then plethysm corresponds to composition of operations.

References

• Littlewood, D.E. (1936), "Polynomial concomitants and invariant matrices", J. London Math. Soc., 11 (1): 49–55, doi:10.1112/jlms/s1-11.1.49, Zbl 0013.14602 
• Littlewood, D. E. (1944), "Invariant theory, tensors and group characters", Philosophical Transactions of the Royal Society A, 239: 305–365, doi:10.1098/rsta.1944.0001, JSTOR 91389, MR 0010594 
• Littlewood, Dudley E. (1950), The theory of group characters and matrix representations of groups, AMS Chelsea Publishing, Providence, RI, ISBN 978-0-8218-4067-2, MR 00002127 
• Littlewood, D. E. (1950b), A University Algebra, Melbourne, London, Toronto: William Heinemann, Ltd., MR 0045079