FishburnTenFiveATree

Abstract

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

Definition 1.1 (Definition Label).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.Label

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.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 state family used in the Fishburn permutation construction.

Definition 1.2 (Definition Paths).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.Paths

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.Paths (✓ 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 A_path_enumeration).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.A_path_enumeration

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.A_path_enumeration (✓ 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.

Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.A_path_enumeration
Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.Label
Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenFiveATree.Paths
Dependency: D5/S3/Combinatorics/Fishburn/FishburnDefs