Burrows-Wheeler transformations and de Bruijn words

We formulate and explain the extended Burrows–Wheeler transform ofMantaci 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 transformwith a view to generating de Bruijn words through inverting the transform. We also make use of de Bruijn words to facilitate a proof that themaximum number of distinct factors of a word of length n has the form 2n 2 − O(n log n). © 2012 Elsevier B.V. All rights reserved.