A394339 Number of unlabeled posemigroups on n elements.

1, 1, 11, 173, 4753, 198838, 13457454, 4207546916

Offset

0,3

Comments

A posemigroup (partially ordered semigroup) is a triple (S, *, <=) where (S, <=) is a partial order, (S, *) is a semigroup (associative binary operation), and * is monotone with respect to <=: for all a, b, x in S, if a <= b then a*x <= b*x and x*a <= x*b.

Links

Table of n, a(n) for n=0..7.

Petr Gajdoš and Martin Kuřil, Ordered semigroups of size at most 7 and linearly ordered semigroups of size at most 10, Semigroup Forum, 89 (2014), 639-663.

Example

a(0) = 0 for n = 0, the unique posemigroup is the empty structure which vacuously satisfies all axioms.

Crossrefs

Cf. A001035, A027851, A394338.

Sequence in context: A133243 A230604 A161355 * A223067 A280442 A218330

Adjacent sequences: A394336 A394337 A394338 * A394340 A394341 A394342

Keyword

nonn,hard,more

Author

Firdous Ahmad Mala, Mar 17 2026

Status

approved