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Finite linear spaces with a regularity condition on the transversals of two secant lines

par Delandtsheer, Anne
Référence European journal of combinatorics, 3, page (119-124)
Publication Publié, 1982

Article révisé par les pairs

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Résumé :

Projective and affine planes are, besides the degenerate projective planes, the only known examples of finite linear spaces for which there is a non-negative integer t such that for any two intersecting lines L, L′ of S and any point p outside L ∪ L′, there are exactly t transversals of L and L′ passing through p. We prove that all finite linear spaces satisfying the above condition are either degenerate projective planes or Steiner systems S(2, k, v) in which t and k must satisfy some rather restrictive arithmetic conditions. © 1982, Academic Press Inc. (London) Limited. All rights reserved.