FishburnTenTenAEnumeration

Abstract

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

Theorem 1.1 (Enumeration of the Fishburn avoidance class).

Lean statement: D5/S3/Combinatorics/Fishburn/FishburnTenTenAEnumeration.a_enumeration

Proof. Machine-checked in Lean as D5/S3/Combinatorics/Fishburn/FishburnTenTenAEnumeration.a_enumeration (✓ 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.

There is one empty Fishburn permutation avoiding 2143, 1423 and 3124. For every positive n, the number of such permutations of length n is n plus twice the binomial coefficient choosing three from n.

References

• Truth anchor: D5/S3/Combinatorics/Fishburn/FishburnTenTenAEnumeration.a_enumeration
• Dependency: D5/S3/Combinatorics/Fishburn/FishburnTenTenACount