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Dirichlet series for finite combinatorial rank dynamics.

Everest, G. and Miles, R. and Stevens, S. and Ward, T. (2010) 'Dirichlet series for finite combinatorial rank dynamics.', Transactions of the American Mathematical Society., 362 (01). pp. 199-227.


We introduce a class of group endomorphisms -- those of finite combinatorial rank -- exhibiting slow orbit growth. An associated Dirichlet series is used to obtain an exact orbit counting formula, and in the connected case this series is shown to have a closed rational form. Analytic properties of the Dirichlet series are related to orbit-growth asymptotics: depending on the location of the abscissa of convergence and the degree of the pole there, various orbit-growth asymptotics are found, all of which are polynomially bounded.

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Publisher statement:First published in Transactions of the American Mathematical Society in 2010, volume 362 published by the American Mathematical Society. © Copyright 2010 American Mathematical Society.
Record Created:12 Oct 2012 10:05
Last Modified:14 Dec 2012 13:56

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