Avoidance by Increasing Blocks

Abstract

A skew sum of increasing blocks avoids 132 and 213.

Theorem 1.1 (Increasing blocks avoid both patterns).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalIncConverse.incBlocks_avoids

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalIncConverse.incBlocks_avoids (✓ 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.

For any list of positive block sizes summing to n, the associated increasing-block permutation avoids both 132 and 213.

References

• Truth anchor: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalIncConverse.incBlocks_avoids
• Dependency: D5/S3/Combinatorics/Nonnesting/NonnestingBasicRoyalIncBlocks