Preece, Donald A. and Anderson, Ian
(2008)
*
Some Z(n+2) terraces from Z(n) power-sequences, n being an odd prime.
*
Discrete Mathematics, 308
(18).
pp. 4086-4107.
ISSN 0012-365X.
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Official URL http://dx.doi.org/10.1016/j.disc.2007.07.110 |

## Abstract

A terrace for Z(m) is an arrangement (a(1), a(2), . . . , a(m)) of the m elements of Z(m) such that the sets of differences a(i +) (1) - a(i) and a(i) - a(i +) (1) (i = 1, 2, . . . , m - 1) between them contain each element of Z(m)\{0} exactly twice. For m odd, many procedures are available for constructing power-sequence terraces for Z(m); each terrace of this sort may be partitioned into segments one of which contains merely the zero element of Z(m), whereas each other segment is either (a) a sequence of successive powers of an element of Z(m) or (b) such a sequence multiplied throughout by a constant. We now extend this idea by using power-sequences in Z(n), where n is an odd prime, to obtain terraces for Z(m) where m = n + 2. Our technique needs each of the n - 1 elements from Z(n)\{0} to be written so as to lie in the interval (0, n) and for three further elements 0, n and n + I then to be introduced. A segment of one of the new terraces may contain just a single element from the set g(0) = {0, n, n +1} or it may be of type (a) or (b) with m = n and containing successive powers of 2, each evaluated modulo n. Also, a segment based on successive powers of 2 may be broken in one, two or three places by putting a different element from g(0) in each break. We provide Z(n+2) terraces for all odd primes n satisfying 0 < n < 1000 except for n = 127, 601, 683.

Item Type: | Article |
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Uncontrolled keywords: | 2-sequencings; number theory; power-sequence terraces; primitive roots |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Jane Griffiths |

Date Deposited: | 18 Apr 2009 10:46 |

Last Modified: | 11 Apr 2014 13:39 |

Resource URI: | https://kar.kent.ac.uk/id/eprint/14711 (The current URI for this page, for reference purposes) |

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