Factorization of permutations

TL;DR

This paper studies how to efficiently factor permutations into a minimal number of special transpositions with bounded distances, connecting to sorting, Cayley graphs, and genomics.

Contribution

It introduces bounds on the number of bounded-distance transpositions needed to factor any permutation, advancing understanding of permutation factorizations.

Findings

Derived bounds on the minimal number of special transpositions

Connected permutation factorization to sorting and genomics applications

Provided insights into Cayley graph structures related to permutations

Abstract

We consider the problem of factoring permutations as a product of special types of transpositions, namely, those transpositions involving two positions with bounded distances. In particular, we investigate the minimum number, $\delta$, such that every permutation can be factored into no more than $\delta$ special transpositions. This study is related to sorting algorithms, Cayley graphs, and genomics.