A bijection between triangulations and $312$-avoiding permutations

TL;DR

This paper establishes a bijection between polygon triangulations and 312-avoiding permutations using ear-clipping, linking geometric structures with combinatorial permutation classes.

Contribution

It introduces a novel bijection connecting polygon triangulations and 312-avoiding permutations via ear-clipping, expanding combinatorial understanding.

Findings

Bijection between triangulations and 312-avoiding permutations

Extension to polygon dissections and related permutation classes

Provides combinatorial tools for geometric and permutation analysis

Abstract

We define a bijection between triangulations of a convex polygon and $312$-avoiding permutations through the process of "ear-clipping". This bijection is then used to obtain a bijection between polygon dissections and a certain class of $312$-avoiding permutations.