# Antimatroids Induced by Matchings

## TL;DR

This paper establishes a deep connection between antimatroids and matchings in bipartite graphs, showing that certain combinatorial structures derived from matchings are exactly antimatroids and vice versa.

## Contribution

It proves that structures induced by stable and maximum-weight matchings are antimatroids and that all antimatroids can be represented through such matchings.

## Key findings

- Structures from stable matchings form antimatroids
- Maximum-weight matchings induce antimatroids
- All antimatroids can be represented by matchings

## Abstract

We explore novel connections between antimatroids and matchings in bipartite graphs. In particular, we prove that a combinatorial structure induced by stable matchings or maximum-weight matchings is an antimatroid. Moreover, we demonstrate that every antimatroid admits such a representation by stable matchings and maximum-weight matchings.