[MONOiD]

4.4 PartialTransMonoid

PartialTransMonoid( n )

PartialTransMonoid returns the monoid of partial transformations of degree n. 

    gap> M:= PartialTransMonoid( 8 );
    Monoid( [ Transformation( [ 2, 1, 3, 4, 5, 6, 7, 8, 9 ] ), 
      Transformation( [ 8, 1, 2, 3, 4, 5, 6, 7, 9 ] ), 
      Transformation( [ 9, 2, 3, 4, 5, 6, 7, 8, 9 ] ), 
      Transformation( [ 2, 2, 3, 4, 5, 6, 7, 8, 9 ] ) ] )
    gap> Size( M );
    1000000000
A partial transformation of degree n is a mapping from {1, ..., n} to itself where every point i in {1, ..., n} has at most one image. Here the undefined point is represented by n+1.

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Version 2.4 (May 1998)
[MONOiD]