In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set X allows us to describe precisely the behaviour of such systems. We can predict by means of closed formulas, the number of gop of the set of all the function from X to itself. We also explore, using the brute force of computers, some subsets of locally rigid functions on X, for which interesting patterns of periodic orbits are found.

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