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FishburnTenSeven

Abstract

Three classes of Fishburn permutations avoiding triples of patterns have a common enumeration.

Theorem 1.1 (Three triple-avoidance enumerations).

Lean statement: D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSeven.result

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

Resolves. Problems/egge-fishburn-conjecture-10-7 (proved) by D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSeven.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 positive n, each of the three classes of Fishburn permutations of length n avoiding respectively 1324, 2143 and 1423; 1324, 2143 and 3124; and 1324, 1423 and 3124 has cardinality two to the power n minus n.

References