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The linearisations of cyclic permutation have rational zeta functions
Published online by Cambridge University Press: 17 April 2009
Abstract
Let n ≥ 2 be an integer. Let P be the set of all integers in [1,n + 1] and let σ be a cyclic permutation on P. Assume that f is the linearisation of σ on P. Then we show that f has rational Artin-Mazur zeta function which is closely related to the characteristic polynomial of some n × n matrix with entries either zero or one. Some examples of non-conjugate maps with the same Artin-Mazur zeta function are also given.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 62 , Issue 2 , October 2000 , pp. 287 - 295
- Copyright
- Copyright © Australian Mathematical Society 2000
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