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FishburnTenTen

Abstract

Fishburn permutations and classical permutations avoiding specified patterns are classified by their forms and permitted insertion positions.

Theorem 1.1 (Equinumerous avoidance classes).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTen.result

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

Resolves. Problems/egge-fishburn-conjecture-10-10 (proved) by D5/S3/Combinatorics/Fishburn/FishburnTenTen.result.

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.

For every nonnegative n, the number of Fishburn permutations of length n avoiding 2143, 1423 and 3124 equals the number of classical permutations of length n avoiding 321, 2143 and 3124, and this number also equals the number of classical permutations of length n avoiding 231, 4132 and 2134.

References