Open Access
May, 1976 Resolvability of Block Designs
Sanpei Kageyama
Ann. Statist. 4(3): 655-661 (May, 1976). DOI: 10.1214/aos/1176343475


The concept of resolvability of a balanced incomplete block (BIB) design, introduced by Bose (1942), was generalized to $\mu$-resolvability of an incomplete block design by Shrikhande and Raghavarao (1964). As a further generalization of these, the concept of $(\mu_1, \mu_2, \cdots, \mu_t$)-resolvability is here introduced for an incomplete block design. This concept may be useful from both combinatorial and practical points of view. Furthermore, some methods of constructing BIB designs with the generalized concept are discussed with illustrations. One method is based on a finite geometry over a Galois field.


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Sanpei Kageyama. "Resolvability of Block Designs." Ann. Statist. 4 (3) 655 - 661, May, 1976.


Published: May, 1976
First available in Project Euclid: 12 April 2007

zbMATH: 0342.05010
MathSciNet: MR403998
Digital Object Identifier: 10.1214/aos/1176343475

Primary: 05B05
Secondary: 05B25 , 62K10

Keywords: $(\mu_1, \mu_2, \cdots, \mu_t)$-resolvability , $\mu$-fold spread , $\mu$-resolvability , $PG(t, q)$ , $PG(t, q): d$ , affine $\mu$-resolvability , association scheme , BIB design , cycle , PBIB design

Rights: Copyright © 1976 Institute of Mathematical Statistics

Vol.4 • No. 3 • May, 1976
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