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A terrace for Z_{m} is a particular type of sequence formed from the m elements of Z_{m}. For m\ud odd, many procedures are available for constructing power-sequence terraces for Z_{m}; each terrace of this\ud sort may be partitioned into segments, of which one contains merely the zero element of Z_{m}, whereas\ud every other segment is either a sequence of successive powers of an element of Z_{m} or such a sequence\ud 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.
I. Anderson and D. A. Preece, Locally balanced change-over designs, Util. Math. 62 (2002), 33-59.
I. Anderson and D. A. Preece, Power-sequence terraces for Zn where n is an odd prime power, Discr. Math. 261 (2003), 31-58.
I. Anderson and D. A. Preece, Some narcissistic half-and-half power-sequence Zn terraces with segments of different lengths, Congr. Numer. 163 (2003), 5-26.
I. Anderson and D. A. Preece, Narcissistic half-and-half power-sequence terraces for Zn with n = pqt, Discr. Math. 279 (2004), 33-60.
I. Anderson and D. A. Preece, Some power-sequence terraces for Zpq with as few segments as possible, Discr. Math. 293 (2005), 29-59.
Soc. B 46 (1984), 323-334.
R. A. Bailey, M. A. Ollis and D. A. Preece, Round-dance neighbour designs from terraces, Discr. Math. 266 (2003), 69-86.
DS10 (available at www.combinatorics.org/surveys/).
M. A. Ollis and D. A. Preece, Sectionable terraces and the (generalised) Oberwolfach problem, Discr. Math. 266 (2003), 399-416.