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FishburnTenTwelvePaths

Abstract

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

Definition 1.1 (Definition PositiveHistory).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.PositiveHistory

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.PositiveHistory (✓ 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 Walk).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.Walk

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.Walk (✓ 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 positive_history_walk).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.positive_history_walk

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.positive_history_walk (✓ 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.

References

  • Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.PositiveHistory
  • Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.Walk
  • Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenTwelvePaths.positive_history_walk
  • Dependency: D5/S3/Combinatorics/Fishburn/FishburnTenTwelveSuccession