The linearisations of cyclic permutation have rational zeta functions
Bau-Sen Du · Bulletin of the Australian Mathematical Society · 2000
Letn≥ 2 be an integer. LetPbe the set of all integers in [1,n+ 1] and let σ be a cyclic permutation onP. Assume thatfis the linearisation of σ onP. Then we show thatfhas rational Artin-Mazur zeta function which is closely related to the characteristic polynomial of somen×nmatrix with entries either zero or one. Some examples of non-conjugate maps with the same Artin-Mazur zeta function are also given.