Realizable Sticky Matroid Conjecture

TL;DR

This paper proves the sticky matroid conjecture and Kantor's conjecture for realizable matroids by establishing a criterion for modular extension of rank-4 hypermodular matroids and demonstrating a related weakening of Kantor's conjecture.

Contribution

It introduces a criterion for modular extension of rank-4 hypermodular matroids and proves a weakened form of Kantor's conjecture for realizable matroids, confirming the conjectures in this case.

Findings

Proves the sticky matroid conjecture for realizable matroids.

Establishes a criterion for modular extension of rank-4 hypermodular matroids.

Demonstrates a weakening of Kantor's conjecture for rank-4 realizable matroids.

Abstract

We give a criterion for modular extension of rank-4 hypermodular matroids, and prove a weakening of Kantor's conjecture for rank-4 realizable matroids. This proves the sticky matroid conjecture and Kantor's conjecture for realizable matroids due to an argument of Bachem, Kern, and Bonin, and due to an equivalence argument of Hochstattler and Wilhelmi, respectively.