On the class of square Petrie matrices induced by cyclic permutations
Let n≥2 be an integer and let P={1,2,…,n,n+1}. Let Zp denote the finite field {0,1,2,…,p−1}, where p≥2 is a prime. Then every map σ on P determines a real n×n Petrie matrix Aσ which is known to contain information on the dynamical properties such as topological entropy and the Artin-Mazur zeta func...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204309026 |
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| _version_ | 1832560462367031296 |
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| author | Bau-Sen Du |
| author_facet | Bau-Sen Du |
| author_sort | Bau-Sen Du |
| collection | DOAJ |
| description | Let n≥2 be an integer and let P={1,2,…,n,n+1}. Let
Zp denote the finite field {0,1,2,…,p−1},
where p≥2 is a prime. Then every map σ on P
determines a real n×n Petrie matrix Aσ which is
known to contain information on the dynamical properties such as
topological entropy and the Artin-Mazur zeta function of the
linearization of σ. In this paper, we show that if
σ is a cyclic permutation on P, then all such
matrices Aσ are similar to one another over Z2 (but
not over Zp for any prime p≥3) and their characteristic
polynomials over Z2 are all equal to ∑k=0nxk. As a
consequence, we obtain that if σ is a cyclic
permutation on P, then the coefficients of the characteristic
polynomial of Aσ are all odd integers and hence nonzero. |
| format | Article |
| id | doaj-art-061c65966143460ca8da841b02e4d9d5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-061c65966143460ca8da841b02e4d9d52025-02-03T01:27:31ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004311617162210.1155/S0161171204309026On the class of square Petrie matrices induced by cyclic permutationsBau-Sen Du0Institute of Mathematics, Academia Sinica, Taipei 11529, TaiwanLet n≥2 be an integer and let P={1,2,…,n,n+1}. Let Zp denote the finite field {0,1,2,…,p−1}, where p≥2 is a prime. Then every map σ on P determines a real n×n Petrie matrix Aσ which is known to contain information on the dynamical properties such as topological entropy and the Artin-Mazur zeta function of the linearization of σ. In this paper, we show that if σ is a cyclic permutation on P, then all such matrices Aσ are similar to one another over Z2 (but not over Zp for any prime p≥3) and their characteristic polynomials over Z2 are all equal to ∑k=0nxk. As a consequence, we obtain that if σ is a cyclic permutation on P, then the coefficients of the characteristic polynomial of Aσ are all odd integers and hence nonzero.http://dx.doi.org/10.1155/S0161171204309026 |
| spellingShingle | Bau-Sen Du On the class of square Petrie matrices induced by cyclic permutations International Journal of Mathematics and Mathematical Sciences |
| title | On the class of square Petrie matrices induced by cyclic permutations |
| title_full | On the class of square Petrie matrices induced by cyclic permutations |
| title_fullStr | On the class of square Petrie matrices induced by cyclic permutations |
| title_full_unstemmed | On the class of square Petrie matrices induced by cyclic permutations |
| title_short | On the class of square Petrie matrices induced by cyclic permutations |
| title_sort | on the class of square petrie matrices induced by cyclic permutations |
| url | http://dx.doi.org/10.1155/S0161171204309026 |
| work_keys_str_mv | AT bausendu ontheclassofsquarepetriematricesinducedbycyclicpermutations |