Half-Flips are 5-Avoidable

Abstract

A word contains a half-flip if it contains non-empty factors [Formula: see text] and [Formula: see text] where [Formula: see text]. 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 [Formula: see text] are 3-avoidable and that half-flips with [Formula: see text] are 2-avoidable.