A general approach to constructing power-sequence terraces for Zn

Anderson, I. and Preece, D. (2008) A general approach to constructing power-sequence terraces for Zn. Discrete Mathematics, 308(5-6), pp. 631-644. (doi:10.1016/j.disc.2007.07.051)

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Publisher's URL: http://dx.doi.org/10.1016/j.disc.2007.07.051

Abstract

A terrace for Z(n) is an arrangement (a(1), a(2),...,a(n)) of the n elements of Z(n) such that the sets of differences a(i+1) - a(i) and a(i) - a(i+1) (i = 1, 2,...,n - 1) between them contain each element of Z(n)\10) exactly twice. For n odd, many procedures have been published for constructing power-sequence terraces for Z(n); each such terrace may be partitioned into segments one of which contains merely the zero element of Z(n) whereas each other segment is either (a) a sequence of successive powers of an element of Z(n) or (b) such a sequence multiplied throughout by a constant. We now present a new general power-sequence approach that yields Z(n) terraces for all odd primes n less than 1000 except for n = 601. It also yields terraces for some groups Z(n) with n = p(2) where p is an odd prime, and for some Z(n) with n = pq where p and q are distinct primes greater than 3. Each new terrace has at least one segment consisting of successive powers of 2, modulo n.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Anderson, Dr Ian
Authors: Anderson, I., and Preece, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Discrete Mathematics
ISSN:0012-365X

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