On semiring complexity of Schur polynomials

TL;DR

This paper investigates the semiring complexity of Schur polynomials, demonstrating that with a fixed number of variables, their complexity grows logarithmically with the largest part of the partition.

Contribution

It establishes a bound on the semiring complexity of Schur polynomials, showing it is logarithmic in the largest partition part when variables are fixed.

Findings

Semiring complexity of Schur polynomials is O(log(λ₁)) with fixed variables.

Complexity depends logarithmically on the largest part of the partition.

Provides bounds relevant for algebraic complexity theory.

Abstract

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 $\lambda$.