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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Cyclic Designs

Wolock, Fred Walter January 1964 (has links)
Cyclic designs are incomplete block designs consisting of sets of blocks where in each set successive blocks are obtained in a cyclic manner from the first block of the set. It is convenient to label the objects (treatments) by the integers 0, 1, …, n-. Then if for a particular set the first block consists of, say, the objects 0, h, i, j, then the second block would contain 1, h+1, i+1, j+1. The remaining blocks in the set are obtained similarly, with reduction modulo n whenever an object label exceeds n-1. A cyclic design consists of such sets or combinations of sets, and will be said to be of size (n, k, r) if the block size is k and the object occurs r times. Cyclic designs are a subclass of partially balanced incomplete block (PBIS) designs. In this dissertation all non-isomorphic designs for combinations of n, k, and r are enumerated, and their efficiencies computed. Non-isomorphic designs are those which are not derivable from any other by a relabeling or permutation of the object labels. A method of analysis is presented which utilizes the cyclic property of the designs. The efficiencies are compared with those of two-associate class PBIB designs and a discussion on the utility of the designs is also given. / Ph. D.

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