A Small Morphism for which the Fixed Point has an Abelian Critical Exponent Less than 2

Abstract

It is known that there are infinite words over finite alphabets with Abelian critical exponent arbitrarily close to 1; however, the construction previously used involves huge alphabets. In this note we give a short cyclic morphism (length 13) over an 8-letter alphabet for which the fixed point has an Abelian critical exponent less than 1.8.