Words with simple Burrows-Wheeler transforms (Q1010806)

Summary: 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.