Pakapongpun, A. and Ward, T. (2009) 'Functorial orbit counting.', Journal of Integer Sequences, 12 . 09.2.4.
We study the functorial and growth properties of closed orbits for maps. By viewing an arbitrary sequence as the orbit-counting function for a map, iterates and Cartesian products of maps define new transformations between integer sequences. An orbit monoid is associated to any integer sequence, giving a dynamical interpretation of the Euler transform.
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