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Classification of Restricted Linear Spaces

Published online by Cambridge University Press:  20 November 2018

Jim Totte
Jim Totte*
Affiliation:
Mathematisches Institut der Universität Tübingen, 74 Tubingeny B.R.D.
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The material in this paper is taken from the author's doctoral dissertation [2]. We will use the terminology and notation of [3]. Let us recall those terms which will be needed here.

We define a restricted linear space (RLS) as a finite set of p elements, called points, of which q subsets, called lines, are distinguished so that the following axioms hold:

(RLS-1) Any two distinct points u, v belong to exactly one common line uv.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 321 - 333
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Dembowski, Peter, Semiaffine Ebenen, Arch. Math. (Basel) 13 (1962), 120–131.Google Scholar
2. Totten, James E., Classification of restricted linear spaces, Ph.D. thesis, University of Waterloo, 1974.Google Scholar
3. Totten, Jim, Basic properties of restricted linear spaces, Discrete Math. 13 (1975), 67–74.Google Scholar
4. Totten, Jim, On the degree of points and lines in a restricted linear space, to appear, Discrete Math.Google Scholar
5. Totten, Jim, Parallelism in restricted linear spaces, to appear, Discrete Math.Google Scholar
6. Totten, Jim and Witte, Paul de, On a Paschian condition for linear spaces, Math. Z. 137 (1974), 173–183.Google Scholar
7. de Witte, Paul, Combinatorial properties of finite plans (in Dutch), Ph.D. thesis, University of Brussels, 1965. Cf. Zbl. 135 (1967), 13–14.Google Scholar
8. de Witte, Paul, Restricted linear spaces with a square number of points, Simon Stevin 1±8 (1975), 107–120.Google Scholar
9. de Witte, Paul, On the embeddability of linear spaces in projective planes of order n, submitted, Trans. Amer. Math. Soc.Google Scholar