The symmetric function theorem via the Fa\`a di Bruno formula
Combinatorics
2022-08-02 v2
Abstract
The symmetric function theorem states that a polynomial that is invariant under permutation of variables, is a polynomial in the elementary symmetric polynomials. We deduce this classical result, in the analytic setting, from the multivariate Fa\`a di Bruno formula. In two variables, this allows us to completely determine all coefficients that occur in the inductive equations.
Cite
@article{arxiv.2207.11241,
title = {The symmetric function theorem via the Fa\`a di Bruno formula},
author = {Siegfried Van Hille},
journal= {arXiv preprint arXiv:2207.11241},
year = {2022}
}
Comments
Added references, small adjustments. Comments welcome!