Cancellative semigroup

TL;DR: The size of the transformation semigroup of a reversible deterministic finite automaton with n states, or equivalently, of a semigroup given by generators of injective partial functions on n objects, is shown to be the maximal size.

TL;DR: An algorithm to compute the set of primitive elements for an embedding dimension three numerical semigroups is given and it is shown how this procedure is used in the study of the construction of L-shapes and the tame degree of the semigroup.