Permutations sortable by n-4 passes through a stack

TL;DR

This paper characterizes and counts permutations sortable by n-4 passes through a stack, proposes a conjecture for n-5 passes, and suggests a polynomial formula for the general case n-k.

Contribution

It provides a detailed characterization and enumeration of permutations sortable by n-4 passes and introduces conjectures and formulas for broader cases.

Findings

Characterization of permutations sortable by n-4 passes

Enumeration results for these permutations

Conjectured formulas for n-5 passes and general n-k case

Abstract

We characterise and enumerate permutations that are sortable by n-4 passes through a stack. We conjecture the number of permutations sortable by n-5 passes, and also the form of a formula for the general case n-k, which involves a polynomial expression.