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.
Cite
@article{arxiv.1901.08392,
title = {Burrows-Wheeler transformations and de Bruijn words},
author = {Peter M. Higgins},
journal= {arXiv preprint arXiv:1901.08392},
year = {2019}
}