Orbit-counting for nilpotent group shifts

MILES, Richard and WARD, Thomas (2008). Orbit-counting for nilpotent group shifts. Proceedings of the American Mathematical Society (PROC), 137, 1499-1507.

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Link to published version:: https://doi.org/10.1090/S0002-9939-08-09649-4


We study the asymptotic behaviour of the orbit-counting function and a dynamical Mertens' theorem for the full G-shift for a finitely-generated torsion-free nilpotent group G. Using bounds for the M{\"o}bius function on the lattice of subgroups of finite index and known subgroup growth estimates, we find a single asymptotic of the shape

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/S0002-9939-08-09649-4
Page Range: 1499-1507
Depositing User: Richard Miles
Date Deposited: 26 Jan 2018 14:22
Last Modified: 18 Mar 2021 16:30
URI: https://shura.shu.ac.uk/id/eprint/17231

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