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Ordering after the First Primitive Block

Abstract

A later inversion creates a cut, restricting primitive words.

Theorem 1.1 (A later inversion forces a cut).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveBlocks.later_inversion_cut

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveBlocks.later_inversion_cut (✓ 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 first occurrences before t are separated from later values but a larger c precedes t, an avoider has a value cut at t minus one.

Theorem 1.2 (Order after an initial one or two).

Lean statement: D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveBlocks.primitive_later_order

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Nonnesting/NonnestingFourPrimitiveBlocks.primitive_later_order (✓ 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.

A primitive avoider beginning with one or two has increasing first-occurrence order among letters from two through n.

References