Dirichlet series for finite combinatorial rank dynamics

EVEREST, Graham, MILES, Richard, STEVENS, Shaun and WARD, Thomas (2010). Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society (TRAN), 362 (1), 199-227.

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Link to published version:: https://doi.org/10.1090/S0002-9947-09-04962-9


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 to be a rational function of exponential variables. 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.

Item Type: Article
Departments - Does NOT include content added after October 2018: Faculty of Social Sciences and Humanities > Department of Teacher Education
Identification Number: https://doi.org/10.1090/S0002-9947-09-04962-9
Page Range: 199-227
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 14:42
Last Modified: 18 Mar 2021 16:30
URI: https://shura.shu.ac.uk/id/eprint/17229

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