Publication at Faculty of Mathematics and Physics |
2016
Abstract
An endomorphism of the free monoid is invertible if it is injective and extends to an automorphism of the free group generated by. A simple example: the endomorphism that leaves all generators invariant except one, say a, which is mapped to ba for some other generator b.
We give a monoid presentation for the submonoid generated by all such endomorphisms when a and b are taken arbitrarily. These left translations are a special case of Nielsen positive transformations: "left" because the mutiplicative constant acts on the left and "positive" because this constant belongs to the free monoid, not the free group.