Koszul-Young Flattenings and Symmetric Border Rank of the Determinant

TL;DR

This paper introduces new lower bounds for the symmetric border rank of the n x n determinant and the 3 x 3 permanent, advancing understanding of their computational complexity.

Contribution

It provides novel lower bounds for the symmetric border rank of the determinant and permanent, improving previous results in algebraic complexity theory.

Findings

New lower bounds for the symmetric border rank of the n x n determinant

Enhanced lower bounds for the 3 x 3 permanent

Progress in algebraic complexity theory

Abstract

We present new lower bounds for the symmetric border rank of the n x n determinant for all n. Further lower bounds are given for the 3 x 3 permanent.