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Row and column orthogonal (0,1)-matrices

✍ Scribed by Adam Berliner; Richard A. Brualdi; Louis Deaett; Kathleen P. Kiernan; Michael Schroeder

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
152 KB
Volume
429
Category
Article
ISSN
0024-3795

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πŸ“œ SIMILAR VOLUMES

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A condition is provided which ensures that a class of (0, 1)-matrices with given row and column sum vectors must contain an asymmetric matrix.

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Let s, t, m, n be positive integers such that sm = tn. Define N (s, t; m, n) to be the number of m Γ— n matrices with entries from {0, 1}, such that each row sum is s and each column sum is t. Equivalently, N(s, t; m, n) is the number of labelled semiregular bipartite graphs, where one colour class c

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Sets of mutually orthogonal systematic row-column designs are constructed, in which treatments from each design are orthogonal to each other and to the entire linear row Γ— columns and quadratic row Γ— columns interaction e ects.