Reduction of the number of associate classes of hypercubic association schemes |
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Authors: | S Kageyama G M Saha A D Das |
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Institution: | (1) Hiroshima University, Hiroshima, Japan;(2) Indian Statistical Institute, India;(3) Jute Agricultural Research Institute, Joydebpur, Bangladesh;(4) Present address: Institute of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil |
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Abstract: | The reduction of the number of associate classes of some hypercubic association schemes by clubbing certain associate classes
has been studied in the paper. It has been found that the reduction of anm-class hypercubic association scheme forv=2
m treatments into a 2-class association scheme is always possible. Further it is proved herein that them-class hypercubic association scheme forv=s
m treatments is reducible (i) to a 3-class association scheme, whens=3 and (ii) to a 2-class association scheme, whens=4, which really hasp
11
1
=p
11
2
and hence leads to a series of balanced incomplete block designs. |
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Keywords: | |
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