A354693 Number of unlabeled prime posets with n elements.

1, 0, 0, 1, 4, 28, 234, 2585, 36326, 646405, 14528011, 412212506

Offset: 1

Author

Salah Uddin Mohammad, Jun 03 2022

Keywords

• nonn
• more

Comments

A poset P is called prime if it is not decomposable. A poset Q is called decomposable if Q can be obtained as the composition (lexicographic product) of the outer poset Q' and the inner posets Qi, 1 <= i <= r, where |Q'| = r > 1 and at least one of the posets Qi is nonsingleton.

Links

• S. M. Khamis, On numerical counting of prime, UPO, and the general type of posets according to heights, Congressus Numerantium, 146 (2000), 157-171.
• S. M. Khamis, Recognition of prime posets and one of its applications, J. Egypt. Math. Soc., 14 (1) (2006), 5-13.

Crossrefs

Cf. A000112, A003430, A202182.