Linear spaces with small generated subspaces |
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Authors: | Peter Dukes Alan CH Ling |
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Institution: | a Department of Mathematics and Statistics, University of Victoria, Victoria, BC V8W 3R4, Canada b Department of Computer Science, University of Vermont, Burlington, Vermont 05405, USA |
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Abstract: | The dimension of a linear space is the maximum positive integer d such that any d of its points generate a proper subspace. Given n, d, s, we consider linear spaces on n points such that any d points generate subspaces of size at most s. Certain design-theoretic constructions and applications are investigated. In particular, one consequence is the existence of proper n-edge-colourings of both Kn+1 (for n odd) and Kn,n with a constant bound on the length of two-colored cycles. |
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Keywords: | Linear space Dimension Pairwise balanced design Subdesign Hä ggkvist numbers |
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