A071536 Number of extensions to a semigroup of the (categorical) composition of arrows in the complete directed graph on n labeled nodes.

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).

Links

Table of n, a(n) for n=0..4.

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

Adjacent sequences: A071533 A071534 A071535 * A071537 A071538 A071539

Keyword

hard,nonn,nice

Author

F. Lockwood Morris (lockwood(AT)ecs.syr.edu), May 29 2002

Status

approved