Is there a common presentation of the semigroup of functions from a given (finite) set to itself?



Presentation of the monoid of self-maps of a finite set
There are several well known presentations. One has to first choose your favorite presentation of the symmetric group. Then one usually adds in a rank n-1 idempotent but some people add all of them or other elements. Then one figures out the extra relations. See [page 161](https://books.google.com/books?id=LC3jxfGEcpYC&pg=PA161) of Classical Finite Semigroups by Ganyushkin and Mazorchuk. You should know the monoid of all self-maps of a set is usually called the full transformation monoid or $T\_n$ when googling. 


Pages 42-43 of <http://research-repository.st-andrews.ac.uk/bitstream/10023/2821/3/NikolaRuskucPhDThesis.pdf> give two presentations. 


