3D permutations and triangle solitaire

TL;DR

This paper establishes a bijection between certain 3D pattern avoiding permutations and triangle bases, linking permutation theory with tilings and TEP subshifts, and resolves a conjecture by Bonichon and Morel.

Contribution

It introduces a novel bijection connecting 3D permutations with triangle bases, bridging permutation patterns and tiling theory, and confirms a prior conjecture.

Findings

Bijection between 3D pattern avoiding permutations and triangle bases

Resolution of Bonichon and Morel's conjecture

Connection established between permutation patterns and tiling theory

Abstract

We provide a bijection between a class of 3-dimensional pattern avoiding permutations and triangle bases, special sets of integer points arising from the theory of tilings and TEP subshifts. This answers a conjecture of Bonichon and Morel.