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FishburnTenTenACount

Abstract

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

Theorem 1.1 (Counting positive insertion positions).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTenACount.a_positive_cut_count

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenTenACount.a_positive_cut_count (✓ 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.

For every n at least two, the number of pairs consisting of a Fishburn permutation of length n avoiding 2143, 1423 and 3124 and a positive insertion position for n plus one that preserves these conditions is one plus twice the binomial coefficient choosing two from n. Insertion positions range from one through n inclusive.

References