Keyboard shortcuts

Press ← or → to navigate between chapters

Press ? to show this help

Press Esc to hide this help

Avoidance under ordinary continuation

Abstract

Let p be a permutation of size n at least two in C whose second entry is less than n and whose first entry is not one more than its second. Then W(p) belongs to C. If n is at least four and p is simple, W(p) is a simple permutation of size n + 1.

Theorem 1.1 (Avoidance under ordinary continuation).

Lean statement: D5/S3/Combinatorics/PopStack/PopStackContinuationAvoidance.ordinary_continuation

Proof. Machine-checked in Lean as D5/S3/Combinatorics/PopStack/PopStackContinuationAvoidance.ordinary_continuation (✓ 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.

Let p be a permutation of size n at least two in C whose second entry is less than n and whose first entry is not one more than its second. Then W(p) belongs to C. If n is at least four and p is simple, W(p) is a simple permutation of size n + 1.

References