Defining relations for idempotent generators in finite full transformation semigroups

In 1966, John Howie showed that the semigroup $mathcal{T}_{n}setminus mathcal{S}_{n}$ of all singular transformations on a n element set is generated by the set of all idempotent transformations of rank n−1. We give a presentation for $mathcal{T}_{n}setminus mathcal{S}_{n}$ in terms of this generating set