The Average Number of Block Interchanges Needed to Sort A Permutation and a recent result of Stanley

TL;DR

This paper derives an explicit formula for the average number of block interchanges required to sort a permutation, utilizing a probabilistic approach related to permutation products.

Contribution

It introduces a novel explicit formula for the average block interchanges needed, based on a probabilistic analysis of permutation products.

Findings

Derived explicit formula for average block interchanges

Connected permutation product properties to sorting complexity

Utilized probabilistic permutation analysis

Abstract

We use an interesting result of probabilistic flavor concerning the product of two permutations consisting of one cycle each to find an explicit formula for the average number of block interchanges needed to sort a permutation of length $n$.