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On the Construction of Cyclic Collineations for Obtaining a Balanced Set of L-Restrictional Prime-Powered Lattice Designs

Sati Mazumdar
The Annals of Mathematical Statistics
Vol. 38, No. 4 (Aug., 1967), pp. 1293-1295
Stable URL: http://www.jstor.org/stable/2238853
Page Count: 3
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
On the Construction of Cyclic Collineations for Obtaining a Balanced Set of L-Restrictional Prime-Powered Lattice Designs
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Abstract

Raktoe [3] has recently developed a procedure for obtaining a balanced confounding scheme for any l-restrictional lattice design of sm treatments where s is a prime or a power of a prime and m is a positive integer. He has shown that the generators of the confounding scheme in each arrangement can be taken from the columns of different powers of the rational canonical form of a matrix of cyclic collineation of a particular order. However, he did not indicate how to construct the generator matrices analytically except for the case s = p = 2. In all other cases, he obtained these matrices empirically. The present paper gives an analytic method for constructing the generator matrices of collineations for all values of s, by the application of a particular theorem in projective geometry and another one from group theory.

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