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A071536
Number of extensions to a semigroup of the (categorical) composition of arrows in the complete directed graph on n labeled nodes.
0
1, 1, 3, 3, 147
OFFSET
0,3
COMMENTS
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).
EXAMPLE
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.
CROSSREFS
Sequence in context: A173127 A230646 A006845 * A094755 A152418 A273925
KEYWORD
hard,nonn,nice
AUTHOR
F. Lockwood Morris (lockwood(AT)ecs.syr.edu), May 29 2002
STATUS
approved