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FishburnTenFiveHistory

Abstract

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

Definition 1.1 (Definition replay).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.replay

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.replay (✓ 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 LegalHistory).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.LegalHistory

Formalization. D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.LegalHistory (✓ 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 maximum_history_equivalence).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.maximum_history_equivalence

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.maximum_history_equivalence (✓ 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/FishburnTenFiveHistory.LegalHistory
  • Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.maximum_history_equivalence
  • Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenFiveHistory.replay
  • Dependency: D5/S3/Combinatorics/Fishburn/FishburnBasicParents