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Dense Near Octagons with Four Points on Each Line, III
Bart De Bruyn
Ghent University, Department of Pure Mathematics and Computer Algebra, Krijgslaan 281 (S22), B-9000 Gent, Belgium
Annals of Combinatorics 15 (1) pp.19-35 January, 2011
AMS Subject Classification: 05B25, 51E12
This is the third paper dealing with the classification of the dense near octagons of order (3; t). Using the artial classification of the valuations of the possible hexes obtained in [12], we are able to show that almost all such near octagons admit a big hex. Combining this with the results in [11], where we classified the dense near octagons of order (3; t) with a big hex, we get an incomplete classication for the dense near octagons of order (3; t): There are 28 known examples and a few open cases. For each open case, we have a rather detailed description of the structure of the near octagons involved.
Keywords: near polygon, near octagon, generalized quadrangle, valuation


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