Exclusion of Large Fixed 231-Avoiders

Abstract

No large sum-indecomposable 231-avoider is fixed by the third iterate.

Theorem 1.1 (The large-size contradiction).

Lean statement: D5/S3/Combinatorics/FundamentalBijection/ThetaCube231LargeFinish.large_edge_collision

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FundamentalBijection/ThetaCube231LargeFinish.large_edge_collision (✓ 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 231-avoiding permutation of size at least eleven fixed by three applications of the inverse fundamental bijection.