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The linearisations of cyclic permutation have rational zeta functions

Published online by Cambridge University Press:  17 April 2009

Bau-Sen Du
Bau-Sen Du
Affiliation:
Institute of Mathematics, Academia Sinica, Taipei, Taiwan 11529, Republic of China, e-mail: [email protected]
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Abstract

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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

References

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