Department of Mathematics
On the rank of cyclic latin squares
Recently, Fang, Shiu ana Pan  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 † Σt 3−1φ(pt ti) where n =Πt−1 x ptti is the prime decomposition of n and φ is the Euler function © 1995, Taylor & Francis Group, LLC. All rights reserved.
Source Publication Title
Linear and Multilinear Algebra
Taylor & Francis
Link to Publisher's Edition
Shiu, W., Fang, K., & Ma, S. (1995). On the rank of cyclic latin squares. Linear and Multilinear Algebra, 40 (2), 183-188. https://doi.org/10.1080/03081089508818433