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FishburnTenSevenClasses

Abstract

Relative orders between three monotone blocks characterize two triple-avoidance classes.

Theorem 1.1 (Avoidance conditions on three blocks).

Lean statement: D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenClasses.shape_classes_iff

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FishburnTenSeven/FishburnTenSevenClasses.shape_classes_iff (✓ 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 D followed by one, I, a peak, and J be a permutation of one through n, with D and J decreasing, I increasing, and every entry of I and J below the peak. It is a Fishburn permutation avoiding 1324, 2143 and 1423 if and only if no entry t of J has t plus one in I and every entry of J is below every entry of D. It is a Fishburn permutation avoiding 1324, 1423 and 3124 if and only if the same successor condition holds and every entry of D below the peak is below every entry of I.

References