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FishburnTenTenAMonotone

Abstract

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

Theorem 1.1 (Monotone permutations and maximum insertion).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTenAMonotone.a_monotone_forms

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenTenAMonotone.a_monotone_forms (✓ 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 nonnegative n, both the increasing and decreasing permutations of one through n are Fishburn permutations avoiding 2143, 1423 and 3124. Among positions zero through n, inserting n plus one into the increasing permutation preserves these conditions exactly at zero or at a position s with n at most s plus one. For the decreasing permutation the permitted positions are exactly zero and n.

References