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Finite Nets, I. Numerical Invariants

Published online by Cambridge University Press:  20 November 2018

R. H. Bruck
R. H. Bruck*
Affiliation:
University of Wisconsin
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A finite net N of degree k, order n, is a geometrical object of which the precise definition will be given in §1. The geometrical language of the paper proves convenient, but other terminologies are perhaps more familiar. A finite affine (or Euclidean) plane with n points on each line is simply a net of degree n+ 1, order n (Marshall Hall [1]). A loop of order n is essentially a net of degree 3, order n (Baer [1], Bates [1]). More generally, for , a set of k —2 mutually orthogonal n ⨯ n latin squares may be used to define a net of degree k, order n (and conversely) by paralleling Bose's correspondence (Bose [1]) between affine planes and complete sets of orthogonal latin squares.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 3 , 1951 , pp. 94 - 107
Copyright
Copyright © Canadian Mathematical Society 1951

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