On the rank functions of $\mathcal{H}$-matroids

TL;DR

This paper characterizes certain $\

Contribution

It introduces a new characterization of some $\

Findings

Provides a rank function-based characterization of $\

Enhances understanding of $\

Connects $\

Abstract

The notion of $\mathcal{H}$-matroids was introduced by U. Faigle and S. Fujishige in 2009 as a general model for matroids and the greedy algorithm. They gave a characterization of $\mathcal{H}$-matroids by the greedy algorithm. In this note, we give a characterization of some $\mathcal{H}$-matroids by rank functions.