Dirichlet series for finite combinatorial rank dynamics

Everest, G, Miles, R, Stevens, S and Ward, T (2010) Dirichlet series for finite combinatorial rank dynamics. Transactions of the American Mathematical Society, 362 (1). pp. 199-227. ISSN 0002-9947

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Abstract

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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics
UEA Research Groups:	Faculty of Science > Research Groups > Number Theory (former - to 2017) Faculty of Science > Research Groups > Algebra and Combinatorics
Related URLs:	http://arxiv.org/abs/0705.1067
Depositing User:	Vishal Gautam
Date Deposited:	18 Mar 2011 14:44
Last Modified:	16 May 2023 00:02
URI:	https://ueaeprints.uea.ac.uk/id/eprint/21081
DOI:	10.1090/S0002-9947-09-04962-9

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