Journal of Integer Sequences, Vol. 12 (2009), Article 09.4.4

A Note on the Relation Between Fixed Point and Orbit Count Sequences

Michael Baake and Natascha Neumärker
Fakultät für Mathematik
Universität Bielefeld
Postfach 100131
33501 Bielefeld


The relation between fixed point and orbit count sequences is investigated from the point of view of linear mappings on the space of arithmetic functions. Spectral and asymptotic properties are derived and several quantities are explicitly given in terms of Gaussian binomial coefficients.

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(Concerned with sequences A000007 A000012 A000203 A001001 A038991 A038992 A038993 A038994 A038995 A038996 A038997 A038998 A038999 and A153038.)

Received December 23 2008; revised version received May 6 2009. Published in Journal of Integer Sequences, May 12 2009.

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