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The structure of the group of permutations induced by Chebyshev polynomial vectors over the ring of integers mod m

Published online by Cambridge University Press:  09 April 2009

Rex Matthews
Rex Matthews
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Tasmania, Australia
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Abstract

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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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 32 , Issue 1 , January 1982 , pp. 88 - 103
Copyright
Copyright © Australian Mathematical Society 1982

References

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