Multiplicative symmetric functions¶
A realization \(h\) of the ring of symmetric functions is multiplicative if for a partition \(\lambda = (\lambda_1,\lambda_2,\ldots)\) we have \(h_\lambda = h_{\lambda_1} h_{\lambda_2} \cdots\).
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sage.combinat.sf.multiplicative.
SymmetricFunctionAlgebra_multiplicative
¶ The class of multiplicative bases of the ring of symmetric functions.
A realization \(q\) of the ring of symmetric functions is multiplicative if for a partition \(\lambda = (\lambda_1,\lambda_2,\ldots)\) we have \(q_\lambda = q_{\lambda_1} q_{\lambda_2} \cdots\) (with \(q_0\) meaning \(1\)).
Examples of multiplicative realizations are the elementary symmetric basis, the complete homogeneous basis, the powersum basis (if the base ring is a \(\QQ\)-algebra), and the Witt basis (but not the Schur basis or the monomial basis).