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International Journal of Mathematics and Mathematical Sciences - Volume 2004 2004, Issue 31, Pages 1617-1622

Institute of Mathematics, Academia Sinica, Taipei 11529, Taiwan

Received 2 September 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let n≥2 be an integer and let P={1,2,…,n,n+1}. LetZp denote the finite field {0,1,2,…,p−1},where p≥2 is a prime. Then every map σ on Pdetermines a real n×n Petrie matrix Aσ which isknown to contain information on the dynamical properties such astopological entropy and the Artin-Mazur zeta function of thelinearization of σ. In this paper, we show that ifσ is a cyclic permutation on P, then all suchmatrices Aσ are similar to one another over Z2 butnot over Zp for any prime p≥3 and their characteristicpolynomials over Z2 are all equal to ∑k=0nxk. As aconsequence, we obtain that if σ is a cyclicpermutation on P, then the coefficients of the characteristicpolynomial of Aσ are all odd integers and hence nonzero.

Author: Bau-Sen Du

Source: https://www.hindawi.com/


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