Excluded minors of interval positroids that are paving matroids

TL;DR

This paper classifies all paving matroids that are excluded minors of interval positroids, showing they can be reduced to three fundamental families and providing a criterion for their characterization.

Contribution

It introduces a reduction method for excluded minors of interval positroids and fully classifies non-positroid paving minors.

Findings

All non-positroid excluded minors of interval positroids are reducible to three fundamental families.

A new criterion characterizes all excluded minors of interval positroids that are paving.

The classification simplifies understanding the structure of these matroids.

Abstract

We prove that every paving matroid that is an excluded minor of interval positroids can be reduced to one of three fundamental families of excluded minors of interval positroids by relaxing dependent hyperplanes. Using this result, we classify all non-positroid excluded minors of interval positroids that are paving matroids. Additionally, we provide a criterion that characterizes all excluded minors of interval positroids that are paving positroids.