# Burrows-Wheeler transformations and de Bruijn words

## TL;DR

This paper explores the extended Burrows-Wheeler transform, linking it to permutations and semigroups, and applies it to generate de Bruijn words by inverting the transform.

## Contribution

It provides a new perspective on the extended Burrows-Wheeler transform using permutation theory and demonstrates its application in generating de Bruijn words.

## Key findings

- Established a link between the extended BWT and cyclic semigroups.
- Provided a method to generate de Bruijn words via inverting the transform.
- Linked syntactic semigroups to the extended BWT.

## Abstract

We formulate and explain the extended Burrows-Wheeler transform of Mantaci et al from the viewpoint of permutations on a chain taken as a union of partial order-preserving mappings. In so doing we establish a link with syntactic semigroups of languages that are themselves cyclic semigroups. We apply the extended transform with a view to generating de Bruijn words through inverting the transform.