How many pop-stacks does it take to sort a permutation?

TL;DR

This paper investigates the number of pop-stacks needed to sort any permutation, providing a new proof that n-1 passes suffice, inspired by classical sorting principles.

Contribution

It offers a novel proof of Unger's result on sorting permutations with pop-stacks, inspired by Knuth's zero-one principle.

Findings

Every permutation of length n can be sorted with n-1 pop-stack passes

A new proof technique based on the zero-one principle is introduced

The result confirms the optimal number of passes needed for sorting with pop-stacks

Abstract

Pop-stacks are variants of stacks that were introduced by Avis and Newborn in 1981. Coincidentally, a 1982 result of Unger implies that every permutation of length n can be sorted by n-1 passes through a deterministic pop-stack. We give a new proof of this result inspired by Knuth's zero-one principle.