Order Around a Maximum

Abstract

Avoidance of 123 and 132 constrains the letters surrounding a maximum.

Theorem 1.1 (Maximum and surrounding letters).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalHooks.maximum_hook_structure

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalHooks.maximum_hook_structure (✓ 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.

In a list of distinct letters avoiding 123 and 132, the letters before its maximum decrease, and every letter before the maximum is larger than every letter after it.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalHooks.maximum_hook_structure
• Dependency: D5/S3/Combinatorics/Nonnesting/NonnestingDefs