FishburnTenFourCLabels

Abstract

Mathematical definitions and results for Fishburn permutations and classical pattern avoidance.

Definition 1.1 (Definition Valley).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.Valley

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.Valley (✓ std3).

Source. Repository-derived.

Acknowledgement. Eric S. Egge (2022). Pattern-Avoiding Fishburn Permutations and Ascent Sequences. DOI: 10.48550/arXiv.2208.01484. URL: https://arxiv.org/abs/2208.01484v1.

Commentary.

This definition specifies a mathematical object used in the Fishburn permutation construction.

Definition 1.2 (Definition label).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.label

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.label (✓ std3).

Source. Repository-derived.

Acknowledgement. Eric S. Egge (2022). Pattern-Avoiding Fishburn Permutations and Ascent Sequences. DOI: 10.48550/arXiv.2208.01484. URL: https://arxiv.org/abs/2208.01484v1.

Commentary.

This definition specifies a mathematical object used in the Fishburn permutation construction.

Theorem 1.3 (Theorem C_count).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.C_count

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenFourCLabels.C_count (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Eric S. Egge (2022). Pattern-Avoiding Fishburn Permutations and Ascent Sequences. DOI: 10.48550/arXiv.2208.01484. URL: https://arxiv.org/abs/2208.01484v1.

Commentary.

This theorem establishes the stated mathematical relation for Fishburn permutations and classical pattern avoidance.