Semiring complexity is the version of arithmetic circuit complexity that allows only two operations: addition and multiplication. We show that semiring complexity of a Schur polynomial $${s_\lambda(x_1,\dots,x_k)}$$sλ(x1,⋯,xk) labeled by a partition $${\lambda=(\lambda_1\ge\lambda_2\ge\cdots)}$$λ=(λ1≥λ2≥⋯) is bounded by $${O(\log(\lambda_1))}$$O(log(λ1)) provided the number of variables k is fixed.

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关于 Schur 多项式的半环复杂度

半灵复杂度是算术电路复杂度的版本，它只允许两种运算：加法和乘法。我们证明了 Schur 多项式的半环复杂度 $${s_\lambda(x_1,\dots,x_k)}$$sλ(x1,⋯,xk) 由分区 $${\lambda=(\lambda_1\ge\ lambda_2\ge\cdots)}$$λ=(λ1≥λ2≥⋯) 以 $${O(\log(\lambda_1))}$$O(log(λ1)) 为界，条件是变量 k 的数量为固定的。