The YY game

TL;DR

This paper introduces a novel single-player game based on planar binary rooted trees, connecting combinatorial mathematics with the four color conjecture through the Tamari poset and associahedron.

Contribution

It presents a new game framework linked to advanced combinatorial structures and explores its mathematical properties related to the four color conjecture.

Findings

Game based on planar binary rooted trees

Connection to the four color conjecture

Use of Tamari poset and associahedron in analysis

Abstract

We introduce a new one-person game similar to the Sudoku game. It is based on combinatorial objects called planar binary rooted trees. It is related to the four color conjecture. Its mathematical analysis makes use of the Tamari poset, hence the Stasheff associahedron.