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Replaceable Nets, Net Collineations, and Net Extensions

Published online by Cambridge University Press:  20 November 2018

T. G. Ostrom
T. G. Ostrom*
Affiliation:
Washington State University
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A net of degree k and order n is a set of n2 points and nk designated sets of points, called lines, such that

  1. (1) The lines fall into k disjoint parallel classes, i.e. each line occurs in exactly one parallel class.

  2. (2) Lines in the same parallel class have no points in common; lines in different parallel classes have exactly one point in common.

  3. (3) Each point lies on exactly one line of each parallel class.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 666 - 672
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. André, J., Über nicht-Desarguesche Ebenen mit transitiver Translationsgruppe, Math. Z., 60 (1954), 156–186.Google Scholar
2. Bose, R. C., Strongly regular graphs, partial geometries, and partially balanced designs, Pacific J. Math., 13 (1963), 389–419.Google Scholar
3. Bruck, R. H., Finite nets, I, Numerical invariants, Can. J. Math., 3 (1951), 94–107.Google Scholar
4. Ostrom, T. G., Semi-translation planes, Trans. Amer. Math. Soc., 111 (1964), 1–18.Google Scholar