# Inverting the Sweep Map on (kn,n)-Dyck Paths: A Simple Algorithm

## TL;DR

This paper presents a simple algorithm that efficiently inverts the sweep map on (kn, n)-Dyck paths for any positive integer k, extending previous methods beyond the (2n, n) case.

## Contribution

The paper introduces a generalized, straightforward algorithm for inverting the sweep map on (kn, n)-Dyck paths applicable to all positive integers k.

## Key findings

- Algorithm successfully inverts the sweep map for all (kn, n)-Dyck paths.
- Extension of previous methods from (2n, n) to arbitrary (kn, n).
- Efficient and simple approach demonstrated through theoretical proof.

## Abstract

We show that our algorithm for inverting the sweep map on (2n, n)-Dyck paths works for any (kn, n)-Dyck path, where k is an arbitrary positive integer.