Separation at Descents

Abstract

A descent separates the values of a permutation avoiding 132 and 213.

Theorem 1.1 (Values on opposite sides of a descent).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalBlocks.descent_separates

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalBlocks.descent_separates (✓ 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 132 and 213, every letter at or before a descent is larger than every letter after that descent.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalBlocks.descent_separates
• Dependency: D5/S3/Combinatorics/Nonnesting/NonnestingDefs