Algorithms for plethysm. (English) Zbl 0556.20013

Chen, Y. M.; Garsia, A. M.; Remmel, J.

Combinatorics and algebra, Proc. Conf., Boulder/Colo. 1983, Contemp. Math. 34, 109-153 (1984).

[For the entire collection see Zbl 0546.00008.]
The authors give a computer practical algorithm for computing the coefficients in the expansion in terms of Schur functions of the plethysm of two Schur functions. By plethysm \(S_{\lambda}[S_{\mu}]\) we mean \(S_{\lambda}(m_ 1,...,m_ n)\) where the \(m_ i\) are monomials with coefficient one and \(S_{\mu}=\sum m_ i\).

Reviewer: David M. Bressoud (Saint Paul)

MSC:

20C30	Representations of finite symmetric groups
20-04	Software, source code, etc. for problems pertaining to group theory
05A17	Combinatorial aspects of partitions of integers

Keywords:

\(\lambda\)-ring of symmetric functions; algorithm; Schur functions; plethysm