# Generalized matrix functions on a linear sum of permutation matrices and their cousins

## TL;DR

This paper introduces a formula for generalized matrix functions of linear sums of permutation matrices, proves they satisfy the permanent dominance conjecture, and extends results to related matrix classes.

## Contribution

The paper provides a new formula for generalized matrix functions on linear sums of permutation matrices and confirms the permanent dominance conjecture for these matrices.

## Key findings

- Derived a formula for generalized matrix functions of linear sums of permutation matrices
- Proved that such matrices satisfy the permanent dominance conjecture
- Extended results to related classes of matrices

## Abstract

A generalized matrix function is a generalization of determinant and permanent function. In this paper, we introduced the formula for the value of a generalized matrix function of a linear sum of permutation matrices. We show that a linear sum of permutation matrices satisfies the permanent dominance conjecture. Finally, we apply the result to some cousins of permutation matrices.