# A new axiom system for matroids: 1. Uniform matroid recognition

## TL;DR

This paper introduces a novel axiom system for matroids based on nonseparable flats and their ranks, providing a polynomial-time algorithm for recognizing uniform matroids, which is otherwise intractable with traditional methods.

## Contribution

The paper presents a new axiomatic framework for matroids and an efficient algorithm for uniform matroid recognition, improving upon existing complexity results.

## Key findings

- Polynomial-time recognition algorithm for uniform matroids
- New axioms based on nonseparable flats and ranks
- Recognition problem is intractable with independence oracles

## Abstract

In this paper, we give a new axioms system based on nonseparable flats with their ranks to define a matroid. We deduce a polynomial time algorithm for deciding if a given matroid (respectively, arbitrary structure) is an uniform matroid. This problem is intractable if we use an independence or an equivalent oracle.