A new lower bound for deterministic pop-stack-sorting

TL;DR

This paper introduces a new lower bound of 3/5 n for the number of sorts needed in a deterministic pop-stack-sorting process, advancing understanding of its efficiency.

Contribution

It establishes a novel lower bound for the deterministic pop-stack-sorting process using a key lemma, improving previous bounds.

Findings

Proves a lower bound of 3/5 n for sorting permutations

Uses a new lemma to analyze the sorting process

Enhances theoretical understanding of pop-stack-sorting efficiency

Abstract

The pop-stack-sorting process is a variation of the stack-sort process. We consider a deterministic version of this process, and provide a new lower bound of $\frac{3}{5}n$ for the number of sorts to fully sort a uniformly randomly chosen permutation via a useful lemma.