The structure of the group of permutations induced by Chebyshev polynomial vectors over the ring of integers mod m
- 1 January 1982
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
- Vol. 32 (1) , 88-103
- https://doi.org/10.1017/s1446788700024435
Abstract
In an earlier paper the author investigated the properties of a class of multivanable polynomial vectors which generalise the multivariable Chebyshev polynomial vectors. In this paper the behaviour of these polynomials over rings of the typeZ/(m) is investigated, and conditions are determined for such an n-variable polynomial vector to induce a permutation of (Z/(m))n. More detailed results on the Chebyshev polynomial vectors follow. The composition properties of these vectors imply that the permutations induced by certain subsets of them form groups under composition of mappings, and the structure of these groups is investigated.Keywords
This publication has 2 references indexed in Scilit:
- The Arithmetical Theory of Linear Recurring SeriesTransactions of the American Mathematical Society, 1933
- The Characteristic Number of a Sequence of Integers Satisfying a Linear Recursion RelationTransactions of the American Mathematical Society, 1931