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Multiplicities and Minimal Widths for (0, 1)-Matrices

Published online by Cambridge University Press:  20 November 2018

D. R. Fulkerson  and
H. J. Ryser
D. R. Fulkerson
Affiliation:
The Rand Corporation
H. J. Ryser
Affiliation:
Ohio State University
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In a previous paper (1) the notion of the α-width ∈A(α) of a (0, 1)-matrix A was introduced, and a formula for the minimal α-width taken over the class of all (0, 1)-matrices having the same row and column sums as A, was obtained. The main tool in arriving at this formula was a block decomposition theorem (1, Theorem 2.1; repeated below as Theorem 2.1) that established the existence, in the class generated by A, of certain matrices having a simple block structure. The block decomposition theorem does not itself directly involve the notion of minimal α-width, but rather centres around a related class concept, that of multiplicity. We review both of these notions in § 2, together with some other pertinent definitions and results.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 14 , 1962 , pp. 498 - 508
Copyright
Copyright © Canadian Mathematical Society 1962

References

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