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The Entry Following the Maximum

Abstract

A successor greater than one is incompatible with the fixed indecomposable 312-avoiding configuration.

Theorem 1.1 (Exclusion of a large successor).

Lean statement: D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Descending.successor_gt_one_absurd

Proof. Machine-checked in Lean as D5/S3/Combinatorics/FundamentalBijection/ThetaCube312Descending.successor_gt_one_absurd (✓ 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.

There is no sum-indecomposable 312-avoiding permutation of size greater than three fixed by the third inverse iterate whose entry immediately after the maximum, read as zero beyond the word, is greater than one.

References