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FishburnTenSevenBEquiv

Abstract

An interval construction produces permutations in the second triple-avoidance class.

Theorem 1.1 (Membership of the second interval form).

Lean statement: D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBEquiv.B_typeII_mem

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBEquiv.B_typeII_mem (✓ 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.

Let two be at most d, d at most h, h less than m, and m at most n. For any Fishburn permutation q of length d minus two avoiding 213, concatenate the decreasing interval from n through m plus one, the decreasing interval from h through d, one, the increasing interval from h plus one through m minus one, m, and q with every entry increased by one. The resulting list is a Fishburn permutation of length n avoiding 1324, 2143 and 3124.

References