Some zn-1 terraces from zn power-sequences, n being an odd prime power

Anderson, I. and Preece, D.A. (2007) Some zn-1 terraces from zn 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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A terrace for Zm is a particular type of sequence formed from the m elements of Zm. For m odd, many procedures are available for constructing power-sequence terraces for Zm; each terrace of this sort may be partitioned into segments, of which one contains merely the zero element of Zm, whereas every other segment is either a sequence of successive powers of an element of Zm 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 Zn can be used to arrange the elements of Zn \ {0} in a sequence of distinct entries i, 1 ≤ i ≤ m, usually in two or more segments, which becomes a terrace for Zm when interpreted modulo m instead of modulo n. Our constructions provide terraces for Zn-1 for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257.

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