Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.4

Functorial Orbit Counting

Apisit Pakapongpun and Thomas Ward
School of Mathematics
University of East Anglia
Norwich NR65LB
United Kingdom


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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(Concerned with sequences A000032 A000041 A000045 A000244 A001047 A006206 A018819 A027377 A027381 A035109 A036987 A038712 A060480 A060648 A065333 and A091574.)

Received October 28 2008; revised version received January 20 2009. Published in Journal of Integer Sequences, February 13 2009.

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