Sorting a Permutation by block moves

TL;DR

This paper establishes bounds on the number of block moves needed to sort permutations, contrasting with block transpositions, and discusses open questions in the field.

Contribution

It provides new theoretical bounds on block moves for permutation sorting and compares these with existing results on block transpositions.

Findings

Established lower and upper bounds on block moves

Contrasted block moves with block transpositions

Raised open questions for future research

Abstract

We prove a lower and an upper bound on the number of block moves necessary to sort a permutation. We put our results in contrast with existing results on sorting by block transpositions, and raise some open questions.