Generalization of a Hadamard type inequality for permanents

TL;DR

This paper extends a Hadamard type inequality for the permanent of complex matrices, providing new bounds and applications, including coefficients of product linear forms and auxiliary inequalities.

Contribution

It introduces a generalized inequality for permanents, extending previous techniques and offering new applications and auxiliary results.

Findings

New inequality for the permanent of complex matrices

Application to coefficients of products of linear forms

Auxiliary inequalities of independent interest

Abstract

This paper is devoted to a generalization of a Hadamard type inequality for the permanent of a complex square matrix. Our proof is based on a non-trivial extension of a technique used in Carlen, Lieb and Loss (Methods and Applications of Analysis 13 (1) (2006) 1-17). We give an application to coefficients of products of linear forms and show some auxiliary inequalities, which might be of independent interest.