Elements of the commutator subgroup of a free group F can be presented as values of canonical forms, called Wicks forms. We show that, starting from sufficiently high genus g, there is a sequence of words wg which can be presented by f(g) distinct Wicks forms, where f(g) > g!. Moreover we may choose these words wg to be square-free.
Cite this article
Andrew J. Duncan, Alina Vdovina, Square-free words as products of commutators. Groups Geom. Dyn. 3 (2009), no. 3, pp. 379–387DOI 10.4171/GGD/62