Anderson, I. and Preece, D.A.
(2007)
Some z_{n-1} terraces from z_{n} power-sequences, n being an odd prime power.
*Proceedings of the Edinburgh Mathematical Society*, 50(3),
pp. 527-549.
(doi: 10.1017/S0013091504000045)

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## Abstract

A terrace for Z_{m} is a particular type of sequence formed from the m elements of Z_{m}. 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, of which one contains merely the zero element of Z_{m}, whereas
every other segment is either a sequence of successive powers of an element of Z_{m} or such a sequence
multiplied throughout by a constant. We now refine this idea to show that, for m=n−1, where n is an odd prime power, there are many ways in which power-sequences in Z_{n} can be used to arrange the elements of Z_{n} \ {0} in a sequence of distinct entries i, 1 ≤ i ≤ m, usually in two or more segments, which becomes a terrace for Z_{m} when interpreted modulo m instead of modulo n. Our constructions provide terraces for Z_{n-1} for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257.

Item Type: | Articles |
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Keywords: | Primary 10A07, secondary 05B30, 2-sequencings, number theory, power-sequence terraces, primitive roots |

Status: | Published |

Refereed: | Yes |

Glasgow Author(s) Enlighten ID: | Anderson, Dr Ian |

Authors: | Anderson, I., and Preece, D.A. |

Subjects: | Q Science > QA Mathematics |

College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |

Journal Name: | Proceedings of the Edinburgh Mathematical Society |

Publisher: | Cambridge University Press |

ISSN: | 0013-0915 |

ISSN (Online): | 1464-3839 |

Published Online: | 08 January 2008 |

Copyright Holders: | Copyright © 2007 Edinburgh Mathematical Society |

First Published: | First published in Proceedings of the Edinburgh Mathematical Society 50(3):527-549 |

Publisher Policy: | Reproduced in accordance with the copyright policy of the publisher |

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