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A071536
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Extensions to a semigroup of the (categorical) composition of arrows in the complete directed graph on n labeled nodes.
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0
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OFFSET
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0,3
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COMMENTS
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Terms obtained, especially the 147, lend some support to the peculiar conjecture that the composition in any category can be extended to a total, associative operation, that is to a semigroup (not, of course, a monoid).
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LINKS
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Table of n, a(n) for n=0..4.
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EXAMPLE
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For n=2, arrows 0:0->0, 1:1->1, f:0->1, g:1->0, the self-dual solution (commutes with reversing arrows) has multiplication table (rows and columns indexed by 0, 1, f, g in order) with rows: 0 f f 0; g 1 1 g; 0 f f 0; g 1 1 g.
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CROSSREFS
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Sequence in context: A173797 A173127 A006845 * A094755 A152418 A113457
Adjacent sequences: A071533 A071534 A071535 * A071537 A071538 A071539
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KEYWORD
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hard,nonn,nice
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AUTHOR
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F. Lockwood Morris (lockwood(AT)ecs.syr.edu), May 29 2002
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STATUS
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approved
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