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

Abstract:

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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