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Ordinary continuation

Abstract

For a word p, W(p) prepends one more than its second entry and increases by one each original entry larger than that second entry. Positions are numbered from zero, and an absent entry is read as zero.

Definition 1.1 (Ordinary continuation).

Lean statement: D5/S3/Combinatorics/PopStack/PopStackContinuation.W

Formalization. D5/S3/Combinatorics/PopStack/PopStackContinuation.W (✓ 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 p, W(p) prepends one more than its second entry and increases by one each original entry larger than that second entry. Positions are numbered from zero, and an absent entry is read as zero.

References