Primitive Two-Prefix Construction

Abstract

A fixed five-letter prefix preserves primitivity under a shifted tail.

Theorem 1.1 (Primitivity after two-prefix insertion).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoConstruct.two_insert_primitive

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoConstruct.two_insert_primitive (✓ 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 a word beginning with one is primitive, replacing its start by 21321 and shifting its remaining letters by two produces a primitive word of size two greater.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoConstruct.two_insert_primitive
• Dependency: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveTwoInsert