Computing with Rational Symmetric Functions and Applications to Invariant Theory and PI-algebras
2010 Mathematics Subject Classification: 05A15, 05E05, 05E10, 13A50, 15A72, 16R10, 16R30, 20G05 Let K be a field of any characteristic. Let the formal power series f(x1, ..., xd) = ∑ αnx1^n1 ··· xd^nd = ∑ m(λ)Sλ(x1, ..., xd), αn, m(λ) ∈ K, be a symmetric function decomposed as a series of Schur functions. When f is a rational function whose denominator is a product of binomials of the form 1−x1^a1 ··· xd^ad, we use a classical combinatorial method of Elliott of 1903 further developed...