Orbit-counting for nilpotent group shifts

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

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Abstract

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

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Departments - Does NOT include content added after October 2018:

Faculty of Social Sciences and Humanities > Department of Teacher Education

Page Range:

1499-1507

Identifiers

Identification Number:

10.1090/S0002-9939-08-09649-4

ORCID:

https://orcid.org/0000-0002-9805-1628