# Transformations of partial matchings

## TL;DR

This paper introduces a novel framework for representing and transforming partial matchings using lattice presentations and polytopes, focusing on minimal-area transformations.

## Contribution

It presents a new method for representing transformations of partial matchings through lattice presentations and associated polytopes, emphasizing minimal-area transformations.

## Key findings

- Introduced lattice presentation for partial matchings
- Defined lattice polytopes for transformation analysis
- Investigated minimal-area transformations

## Abstract

We consider partial matchings, which are finite graphs consisting of edges and vertices of degree zero or one. We consider transformations between two states of partial matchings. We introduce a method of presenting a transformation between partial matchings. We introduce the notion of the lattice presentation of a partial matching, and the lattice polytope associated with a pair of lattice presentations, and we investigate transformations with minimal area.