Symmetric skew balanced starters and complete balanced Howell rotations
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- by Ding Zhu Du and F. K. Hwang PDF
- Trans. Amer. Math. Soc. 271 (1982), 409-413 Request permission
Abstract:
Symmetric skew balanced starters on $n$ elements have been previously constructed for $n = 4k + 3$ a prime power and $8k + 5$ a prime power. In this paper we give an approach for the general case $n = {2^m}k + 1$ a prime power with $k$ odd. In particular we show how this approach works for $m = 2$ and $3$. Furthermore, we prove that for $n$ of the general form and $k > 9 \cdot {2^{3m}}$, then a symmetric skew balanced starter always exists. It is known that a symmetric skew balanced starter on $n$ elements, $n$ odd, can be used to construct complete balanced Howell rotations (balanced Room squares) for $n$ players and $2(n + 1)$ players, and in the case that $n$ is congruent to $3$ modulo $4$, also for $n + 1$ players.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 271 (1982), 409-413
- MSC: Primary 05B15; Secondary 05B10, 90D12
- DOI: https://doi.org/10.1090/S0002-9947-1982-0654840-8
- MathSciNet review: 654840