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September, 1963 Right Angular Designs
Suresh K. Tharthare
Ann. Math. Statist. 34(3): 1057-1067 (September, 1963). DOI: 10.1214/aoms/1177704030


Known PBIB designs with two associate classes were classified according to their association schemes by Bose and Shimamoto [3]. Association schemes for three or more associate classes have been little developed except the rectangular association scheme of Vartak [15] and GD $m$-associate designs of Raghavaroa [8] and Hierarchical group divisible designs with $m$-associate classes of Roy [11]. In this paper we define a new association scheme known as right angular scheme which defines four associate class designs. For convenience we call PBIB designs with right angular scheme, right angular designs. In Section 2 we define the association scheme. Sections 4 and 5 deal with the analysis and construction of right angular designs. In Section 6 we study some combinatorial properties and Sections 3 and 7 give the non-existence of some right angular designs.


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Suresh K. Tharthare. "Right Angular Designs." Ann. Math. Statist. 34 (3) 1057 - 1067, September, 1963.


Published: September, 1963
First available in Project Euclid: 27 April 2007

zbMATH: 0119.35103
MathSciNet: MR152074
Digital Object Identifier: 10.1214/aoms/1177704030

Rights: Copyright © 1963 Institute of Mathematical Statistics

Vol.34 • No. 3 • September, 1963
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