Cartesian Decomposition of fixed shape [00E5]

    Recall the definition of the cartesian decomposition

    Definition 1. cartesian decomposition [00DQ]

      Given a finite set , we define the type of cartesian decompositions by

      Where cartesian product in FinSet.

      hello world

      Definition 2. cartesian decomposition of fixed shape [00E7]

        Define

        We can view the as

        write for .

        Now the acts on by

        Transitivity (there is only one orbit)

        Consider two decompositions