An Improved Lower Bound for Stack Sorting

TL;DR

This paper improves the theoretical lower bound on the number of stacks needed to sort n elements, advancing understanding in the combinatorial problem of stack sorting.

Contribution

It presents a new asymptotic lower bound of 0.561 log_2 n + O(1), surpassing the previous 0.5 log_2 n + O(1) bound from 1972.

Findings

New lower bound of 0.561 log_2 n + O(1) for stack sorting

First significant improvement since 1972

Advances theoretical understanding of stack sorting complexity

Abstract

We consider the problem of sorting elements on a series of stacks, introduced by Tarjan and Knuth. We improve the asymptotic lower bound for the number of stacks necessary to sort $n$ elements to $0.561 \log_2 n + O(1)$. This is the first significant improvement since the previous lower bound, $1/2 \log_2 n + O(1)$, was established by Knuth in 1972.