Half-flips Are 5-Avoidable

A word contains a half-flip if it contains non-empty factors uv and vu where |u|=|v|. Fici reports a non-constructive proof of the existence of an infinite word over a finite alphabet avoiding half-flips and asks for the size of the smallest alphabet over which half-flips may be avoided. Currie and Rampersad have proposed a pure morphic word over 8 letters and a morphic word over 5 letters and conjecture that they avoid half-flips. We present a pure morphic word over 5 letters that avoids half-flips. We also show that half-flips with |u|≥2 are 3-avoidable and that half-flips with |u|≥4 are 2-avoidable.