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Realizability of Integer Sequences as Differences of Fixed Point Count Sequences
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Natascha Neumärker

Fakultät für Mathematik

Universität Bielefeld

Postfach 100131

33501 Bielefeld

Germany

**Abstract:**

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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