Plumbing bijections

TL;DR

This paper explores the invariance of water system outputs in Yoshi Hill despite different configurations of crossings, illustrating a form of bijection in plumbing systems.

Contribution

It introduces a novel perspective on bijections in plumbing systems, demonstrating their invariance properties regardless of crossing configurations.

Findings

Water system outputs are invariant under different crossing arrangements.

Bijections can be used to model and analyze plumbing system configurations.

The approach provides insights into system robustness and design flexibility.

Abstract

The legendary Mario and Luigi show us that whether you slap in the crossings as early as a warp pipe can shoot you or as late as the very last bend, the water system in Yoshi Hill comes out exactly the same!