Enumerating Motzkin–Rabin geometries |
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| Authors: | Paul van Wamelen |
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| Institution: | Department of Mathematics, Louisiana State University, Baton Rouge, Los Angeles, CA 70803‐4918 |
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| Abstract: | The main result of this paper is an enumeration of all Motzkin‐Rabin geometries on up to 18 points. A Motzkin‐Rabin geometry is a two‐colored linear space with no monochromatic line. We also study the embeddings of Motzkin‐Robin geometries into projective spaces over fields and division rings. We find no Motzkin‐Rabin geometries on up to 18 points embeddable in ?2 or ??2(t)2. We find many examples of Motzkin‐Rabin geometries with no proper linear subspaces. We give an example of a proper linear space embeddable in ?(?( )2). © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 179–194, 2007 |
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| Keywords: | finite linear spaces Motzkin– Rabin geometries enumeration |
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