Size Bound for Indecomposable Fixed 312-Avoiders

Abstract

Sum-indecomposable 312-avoiders fixed by the third iterate have size at most three.

Theorem 1.1 (Exclusion beyond size three).

Lean statement: D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Classify.fixed312_large_absurd

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Classify.fixed312_large_absurd (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Kassie Archer, Robert P. Laudone (2024). Pattern avoidance and the fundamental bijection. DOI: 10.48550/arXiv.2407.06338. URL: https://arxiv.org/abs/2407.06338v1.

Commentary.

There is no sum-indecomposable 312-avoiding permutation of size greater than three fixed by three applications of the inverse fundamental bijection.