# Nonnegative sum-symmetric matrices, optimal-score partitions, and optimal resource allocation

## TL;DR

This paper investigates optimal resource allocations through the lens of nonnegative sum-symmetric matrices, revealing that such matrices can be decomposed into circuit matrices, leading to insights on optimal-score partitions.

## Contribution

It introduces a novel representation of nonnegative sum-symmetric matrices as sums of circuit matrices, facilitating the analysis of optimal-score partitions and resource allocation.

## Key findings

- Nonnegative sum-symmetric matrices can be decomposed into circuit matrices.
- Optimal-score partitions correspond to certain resource allocation strategies.
- The decomposition aids in understanding the structure of optimal solutions.

## Abstract

The main result of the note describes certain optimal-score partitions, which can be interpreted as optimal resource allocations. This result is based on the fact that any nonnegative square matrix whose column sums are the same as the corresponding row sums can be represented as the sum of circuit matrices.