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August, 1967 On the Construction of Cyclic Collineations for Obtaining a Balanced Set of $L$-Restrictional Prime-Powered Lattice Designs
Sati Mazumdar
Ann. Math. Statist. 38(4): 1293-1295 (August, 1967). DOI: 10.1214/aoms/1177698803

Abstract

Raktoe [3] has recently developed a procedure for obtaining a balanced confounding scheme for any $l$-restrictional lattice design of $s^m$ 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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Sati Mazumdar. "On the Construction of Cyclic Collineations for Obtaining a Balanced Set of $L$-Restrictional Prime-Powered Lattice Designs." Ann. Math. Statist. 38 (4) 1293 - 1295, August, 1967. https://doi.org/10.1214/aoms/1177698803

Information

Published: August, 1967
First available in Project Euclid: 27 April 2007

zbMATH: 0155.27001
MathSciNet: MR215453
Digital Object Identifier: 10.1214/aoms/1177698803

Rights: Copyright © 1967 Institute of Mathematical Statistics

Vol.38 • No. 4 • August, 1967
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