IDA: Gapplet

Gapplet

Let S_n be the monoid (actually, a group) of all invertible maps {1,...,n} -> {1,...,n}. Write

m =

Then there is a morphism f : S_n -> S_m given by

f(g)({i,j}) = {g(i),g(j)}.

Later, we shall come back to this morphism. Here, we describe the image under f of an element you input.

Input a list, representing an element of S_n, e.g., [1,4,3,5,6,2] in case n = 6

Determine its image in S_m