A376633 T(n,k) is the number of nonisomorphic n-element self-dual posets (or partially ordered sets) with k arcs in the Hasse diagram, irregular triangle read by rows.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 5, 2, 1, 1, 1, 2, 4, 9, 11, 12, 5, 4, 1, 1, 1, 2, 4, 10, 16, 26, 22, 21, 10, 5, 0, 1, 1, 1, 2, 4, 11, 20, 44, 65, 98, 86, 79, 41, 25, 8, 4, 2, 2, 1, 1, 2, 4, 11, 21, 51, 92, 175, 220, 276, 237, 208, 103, 67, 25, 18, 5, 3, 0, 1, 1, 1, 2, 4, 11, 22, 55, 114, 264, 462, 798, 1015, 1294, 1180, 1035, 676, 477, 243, 149, 57, 36, 13, 8, 2, 4, 1, 1, 1, 2, 4, 11, 22, 56, 121, 303, 614, 1264, 2042, 2348, 3995, 4755, 4272, 3910, 2680, 1977, 1078, 697, 300, 189, 60, 50, 15, 12, 0, 3, 0, 1

Offset

1,9

Comments

Posets whose Hasse diagram looks the same if it is turned upside down.

The dual poset P* of the poset P is defined by: s ≤ t in P* if and only if t ≤ s in P. If P and P* are isomorphic, then P is called self-dual.

References

R. P. Stanley, Enumerative Combinatorics I, 2nd. ed., pp. 277.

Links

Table of n, a(n) for n=1..136.

Example

The table starts:
1 ;
1 1 ;
1 1 1 ;
1 1 2 2 2 ;
1 1 2 3 5 2 1 ;
1 1 2 4 9 11 12 5 4 1 ;
1 1 2 4 10 16 26 22 21 10 5 0 1 ;
1 1 2 4 11 20 44 65 98 86 79 41 25 8 4 2 2 ;
1 1 2 4 11 21 51 92 175 220 276 237 208 103 67 25 18 5 3 0 1 ;
1 1 2 4 11 22 55 114 264 462 798 1015 1294 1180 1035 676 477 243 149 57 36 13 8 2 4 1;
...

Crossrefs

Cf. A000112, A022016, A022017, A342447.

Row sums: A133983.

Sequence in context: A356997 A171412 A248213 * A317682 A216651 A071338

Adjacent sequences: A376630 A376631 A376632 * A376634 A376635 A376636

Keyword

nonn,tabf

Author

Rico Zöllner and Konrad Handrich, Sep 30 2024

Status

approved