Avoidance after Two-Prefix Insertion

Abstract

The 21321 insertion preserves the four-pattern avoidance class.

Theorem 1.1 (Two-prefix insertion preserves avoidance).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoInsert.two_insert

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoInsert.two_insert (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Sergi Elizalde, Amya Luo (2024). Pattern avoidance in nonnesting permutations. DOI: 10.48550/arXiv.2412.00336. URL: https://arxiv.org/abs/2412.00336v6.

Commentary.

If an avoider begins with one, replacing its start by 21321 and shifting the remaining letters by two yields an avoider of size two greater.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoInsert.two_insert
• Dependency: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoTail