A373456 Number of tree interval posets of permutations of size n, considered up to isomorphism.

1, 1, 1, 3, 6, 14, 32, 79, 192, 488, 1244, 3240, 8497, 22561, 60309, 162541, 440598, 1201377, 3291426, 9058464, 25027797, 69401101, 193071153, 538724060, 1507288378, 4227824974, 11886150870, 33488522111, 94539554742, 267383598840, 757539956852, 2149698586706, 6109515731611

Offset: 1

Author

Mathilde Bouvel, Jun 06 2024

Keywords

• nonn

Comments

See Remark 24 in [Bouvel-Cioni-Izart].

References

• Bridget E. Tenner. Interval Posets of Permutations. Order, 39(3):523-536, 2022.

Links

• Mathilde Bouvel, Lapo Cioni, and Benjamin Izart, The interval posets of permutations seen from the decomposition tree perspective, arXiv:2110.10000 [math.CO], 2021-2024.
• Bridget E. Tenner, Interval Posets for Permutations, arXiv:2007.06142 [math.CO], 2020-2021.

Crossrefs

For the same posets but not considered up to isomorphism, see A054515.

For interval posets that are not necessarily trees, see A373455 (for posets also considered up to isomorphism) and A348479 (otherwise).

Formula

Asymptotic behavior of a(n) is c*n^(-3/2)*r^n with c approximately 0.2597 and r approximately 2.9784. See M. Bouvel, L. Cioni, B. Izart (Remark 24).