Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.5

Realizability of Integer Sequences as Differences of Fixed Point Count Sequences

Natascha Neumärker
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
33501 Bielefeld


A sequence of non-negative integers is exactly realizable as the fixed point counts sequence of a dynamical system if and only if it gives rise to a sequence of non-negative orbit counts. This provides a simple realizability criterion based on the transformation between fixed point and orbit counts. Here, we extend the concept of exact realizability to realizability of integer sequences as differences of the two fixed point counts sequences originating from a dynamical system and a topological factor. A criterion analogous to the one for exact realizability is given and the structure of the resulting set of integer sequences is outlined.

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(Concerned with sequences A000004 A000007 A000012 A000048 A000225 A001350 A001610 A060280 A099430.)

Received April 22 2009; revised version received May 8 2009. Published in Journal of Integer Sequences, May 12 2009.

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