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Inserting a minimum in an early gap

Abstract

For a word with positive entries, add one to every value and insert one into any existing gap of zero-based index at most two. The resulting word belongs to C if and only if the original word belongs to C.

Theorem 1.1 (Inserting a minimum in an early gap).

Lean statement: D5/S3/Combinatorics/PopStack/PopStackMinimum.minimum_insertion_inC

Proof. Machine-checked in Lean as D5/S3/Combinatorics/PopStack/PopStackMinimum.minimum_insertion_inC (✓ std3). ∎

Source. Repository-derived.

Acknowledgement. Lapo Cioni, Luca Ferrari, Rebecca Smith (2025). Sorting permutations using a pop stack with a bypass. DOI: 10.1016/j.disc.2025.114964. URL: https://arxiv.org/abs/2503.08285v1.

Commentary.

For a word with positive entries, add one to every value and insert one into any existing gap of zero-based index at most two. The resulting word belongs to C if and only if the original word belongs to C.

References