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The Pair before the Terminal Configuration

Abstract

Avoidance and a cyclic successor determine two additional suffix entries.

Theorem 1.1 (Two forced suffix entries).

Lean statement: D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Suffix.terminal_pair_positions

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Suffix.terminal_pair_positions (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Kassie Archer, Robert P. Laudone (2024). Pattern avoidance and the fundamental bijection. DOI: 10.48550/arXiv.2407.06338. URL: https://arxiv.org/abs/2407.06338v1.

Commentary.

For a 312-avoiding permutation of size n at least seven ending with n minus one, two, n, one and having cyclic successor n minus three for the letter three, the entries at positions n minus six and n minus five are three and n minus two.

References