Kr\"auter conjecture on permanents is true

TL;DR

This paper proves Kr"auter conjecture by establishing a sharp upper bound for the permanent of (-1,1)-matrices over fields of zero characteristic, based on matrix rank, thus solving a problem posed in 1974.

Contribution

It confirms Kr"auter conjecture and provides a precise upper bound for the permanent of (-1,1)-matrices depending on their rank.

Findings

Confirmed Kr"auter conjecture

Established sharp upper bounds for permanents

Solved Wang's 1974 problem

Abstract

In this paper we investigate the permanent of $(-1,1)$-matrices over fields of zero characteristics and our main goal is to provide a sharp upper bound for the value of the permanent of such matrices depending on matrix rank, solving Wang's problem posed in 1974 by confirming Kr\"auter conjecture formulated in 1985.