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Finite Incidence Structures with Orthogonality

  • F. A. Sherk (a1)

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An incidence structure consists of two sets of elements, called points and blocks, together with a relation, called incidence, between elements of the two sets. Well-known examples are inversive planes, in which the blocks are circles, and projective and affine planes, in which the blocks are lines. Thus in various examples of incidence structures, the blocks may have various interpretations. Very shortly, however, we shall impose a condition (Axiom A) which ensures that the blocks behave like lines. In anticipation of this, we shall refer to the set of blocks as the set of lines. Also, we shall employ the usual terminology of incidence, such as “lies on,” “passes through,” “meet,” “join.” etc.

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References

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1. Bachmann, F., Aufbau der Geometrie aus dem Spiegelungsbegriff, Grundlehren der Math. Wiss. 96 (Berlin, 1959).
2. Baer, R., Polarities infinite projective planes, Bull, Amer. Math. Soc., 52 (1946), 7793.
3. Hall, Marshall Jr., The theory of groups (New York, 1959).
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Finite Incidence Structures with Orthogonality

  • F. A. Sherk (a1)

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