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A100001
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Number of self-dual combinatorial configurations of type (n_3).
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3
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0, 0, 0, 0, 0, 0, 1, 1, 3, 10, 25, 95, 366, 1433, 5802, 24105, 102479, 445577, 1992044
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OFFSET
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1,9
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COMMENTS
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A combinatorial configuration of type (n_3) consists of an (abstract) set of n points together with a set of n triples of points, called lines, such that each point belongs to 3 lines and each line contains 3 points.
Interchanging the roles of points and lines gives the dual configuration. A configuration is self-dual if there is an isomorphism from it to its dual.
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LINKS
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EXAMPLE
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Example: the Fano plane is the only (7_3) configuration and is self-dual. It contains 7 points 1,2,...7 and 7 triples, 124, 235, 346, 457, 561, 672, 713.
The unique (8_3) configuration is also self-dual. It consists of the triples 125, 148, 167, 236, 278, 347, 358, 456.
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CROSSREFS
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KEYWORD
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nonn,nice,hard,more
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AUTHOR
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EXTENSIONS
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a(1)-a(18) from the Betten, Brinkmann and Pisanski article.
a(19) from the Pisanski et al. article.
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STATUS
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approved
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