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Enumerating Motzkin–Rabin geometries
Author(s) -
van Wamelen Paul
Publication year - 2007
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20119
Subject(s) - mathematics , linear subspace , combinatorics , monochromatic color , division (mathematics) , enumeration , space (punctuation) , discrete mathematics , geometry , arithmetic , computer science , botany , biology , operating system
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 ℂ 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 ℙ(ℚ( $\sqrt -7$ ) 2 ). © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 179–194, 2007