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FishburnTenSevenBParameters

Abstract

The second triple-avoidance class has parameters describing initial-one tails and interval forms.

Definition 1.1 (Permutations starting with one).

Lean statement: D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBParameters.HStart

Formalization. D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBParameters.HStart (✓ 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 a nonnegative size, this set consists of the Fishburn permutations of that length avoiding 213 whose first entry is one.

Definition 1.2 (Parameters for the second class).

Lean statement: D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBParameters.BParameters

Formalization. D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenBParameters.BParameters (✓ 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.

Choose a maximum between one and the size. Its parameters are the disjoint union of Fishburn permutations of length maximum avoiding 213 and starting with one, and triples consisting of a low between two and maximum minus one, a high between low and maximum minus one, and a Fishburn permutation of length low minus two avoiding 213.

References