科研成果详情

Recently, Fang, Shiu ana Pan [3] suggested a new way to generate uniform designs based on cyclic Latin squares The new designs have better uniformity than some other known uniform designs. In their paper, Fang, Shiu and Pan indicated that the rank of the cyclic Latin squares used in the construction of uniform designs is important and they wanted to know the maximum and the minimum possible values of the rank of all cyclic Latin squares. In this paper we prove that the maximum value of the rank of cyclic Latin squares of order n is n while the minimum value is 1 † Σt3−1φ(ptti) where n =Πt−1x ptti is the prime decomposition of n and φ is the Euler function © 1995, Taylor & Francis Group, LLC. All rights reserved.