Proofs

Abstract

Let σ_a(z) denote ${{1 - z^a } \over {1 - z}}{{z^{(1 - a)/2} } \over a}$, so that $\sigma _{a^2 } (z) = {{1 - z^{a^2 } } \over {1 - z}}{{z^{(1 - a^2 )/2} } \over {a^2 }}$and let the symmetric symbol of a scheme of arity a be $f(z) = (\sigma _a (z))^m k_a (z)$where k_a(z) is a symmetric Laurent polynomial not divisible by σ_a(z), and whose coefficients sum to a.