On the Range of the Permanent of $(\pm1)$-Matrices

TL;DR

This paper proves a superpolynomial lower bound on the diversity of the permanent values for matrices with entries of plus or minus one, highlighting the complexity of this mathematical function.

Contribution

It establishes a superpolynomial lower bound on the range of the permanent for $\pm1 ext{-matrices}$, advancing understanding of the function's complexity.

Findings

Superpolynomial lower bound on the permanent range.

Highlights complexity of $\pm1 ext{-matrices}$.

Advances theoretical understanding of matrix permanents.

Abstract

We establish a superpolynomial lower bound on the range of the permanent function on the set of $n\times n$ matrices with $\pm1$ entries.