A361920 Number of unlabeled ranked posets with n elements.

1, 1, 2, 5, 16, 61, 280, 1501, 9394, 68647, 591570, 6108298, 77162708, 1219779207, 24648006828, 647865966973, 22437052221282, 1032905858402302, 63591727342096158, 5258562027225785955, 586001891321599337103, 88241281449605821921186, 17996565026907866304071630

Offset: 0

Author

Martin Rubey, Mar 29 2023

Keywords

• nonn

Comments

A partially ordered set is ranked if there is a function from the poset elements to the integers such that the function value of a covering element is precisely one larger than the function value of the covered element. This is called graded by some authors.

Examples

			For n=5, A000112(n) - a(n) = 63 - 61 = 2 because we have 2 posets with 5 elements that are not ranked: a<b<c<d  a<e<d  and  a<c<e  a<d  b<d  b<e where < means "is covered by". - _Geoffrey Critzer_, Oct 29 2023
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..40

Crossrefs

Row sums of A361953.

Cf. A000112, A001833 (labeled), A223911, A361912, A361955.

Programs

PARI

\\ See PARI link in A361953 for program code.
A361920seq(20) \\ Andrew Howroyd, Apr 01 2023

Sage

sum(1 for P in posets(n) if P.is_ranked())

Extensions

Terms a(8) and beyond from Andrew Howroyd, Mar 31 2023