Words with Simple Burrows-Wheeler Transforms

Abstract

Mantaci et al have shown that if a word $x$ on the alphabet $\{a,b\}$ has a Burrows-Wheeler Transform of the form $b^ia^j$ then $x$ is a conjugate or a power of a conjugate of a standard word. We give an alternative proof of this result and describe words on the alphabet $\{a,b,c\}$ whose transforms have the form $c^ib^ja^k$. These words have some common properties with standard words. We also present some results about words on larger alphabets having similar properties.