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Matrix Rational Completions Satisfying Generalized Incidence Equations

Published online by Cambridge University Press:  20 November 2018

E. C. Johnsen
E. C. Johnsen*
Affiliation:
The Ohio State University and The University of California, Santa Barbara
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Let us consider the following problem. Let there be v elements x1 , . . . , xv and v sets S1, . . . , Sv such that every set contains exactly k distinct elements and every pair of sets has exactly λ distinct elements in common. To avoid trivial situations we shall in general assume that 0 < λ < k < v — 1. This is known as a v, k, λconfiguration or design. We can give an equivalent characterization of a configuration in terms of a matrix A = [aij], called its incidence matrix, by writing the elements x1 , . . . , xv row and the sets S1, . . . , Sv in a column and setting aij = 1 if xj is in Si and aij = 0 if xj is not.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 1 - 12
Copyright
Copyright © Canadian Mathematical Society 1965

References

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