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Equi‐replicated balanced block designs generated by a balanced matrix
Author(s) -
Brzeskwiniewicz H.
Publication year - 1982
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710240521
Subject(s) - block (permutation group theory) , combinatorics , integer (computer science) , incidence matrix , matrix (chemical analysis) , mathematics , block design , arithmetic , physics , computer science , chemistry , chromatography , quantum mechanics , node (physics) , programming language
In this paper it is shown that if N * h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c ih N ih , where c ih are some non‐negative integer numbers and N ih are such incidence matrices that A h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N ih is a balanced matrix defined by S HAH (1959), for h = 1, 2,…, p , then a block design with an incidence matrix Ñ = [ N * 1 , N * 2 ,…, N * p ] is an equi‐replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M 0 introduced by C ALIŃSKI (1971).