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

Journal of the Australian Mathematical Society

Rex Matthews¹ 

关键词: 12 C 05;    12 C 30;   

DOI  :  10.1017/S1446788700024435

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

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.

【 授权许可】

Unknown