2022/07/22 by Siegfried Van Hille, Van Hille, Siegfried
Physics and Astronomy · Mathematics · #Advanced Mathematical Theories and Applications #Advanced Combinatorial Mathematics
paper · pdf · doi:10.48550/arxiv.2207.11241
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 Faà di Bruno formula. In two variables, this allows us to completely determine all coefficients that occur in the inductive equations.