On semiring complexity of Schur polynomials
  Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that when the number of variables is fixed, the semiring complexity of a Schur polynomial $s_\lambda$ is $O(log(\lambda_1))$; here $\lambda_1$ is the largest part of the partition $\lambda$. 
Sergey Fomin, Dima Grigoriev, Dorian Nogneng, Eric Schost
cs.CC math.CO