On the maximum of the permanent of (I-A)

TL;DR

This paper establishes an upper bound for the permanent of (I-A) where A is a doubly substochastic matrix, based on the matrix size and the sum of its elements, contributing to matrix theory and combinatorics.

Contribution

It provides a new upper bound for the permanent of (I-A) considering the size and total sum of A's elements, extending previous bounds in matrix analysis.

Findings

Derived an explicit upper bound for perm(I-A)

Bound depends on matrix size n and sum of elements σ(A)

Enhances understanding of permanents in doubly substochastic matrices

Abstract

Let A be an n by n doubly substochastic matrix and denote {\sigma}(A) the sum of all elements of A. In this paper we give the upper bound of the permanent of (I-A) with respect to n and {\sigma}(A).