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

Author

Rico Zöllner and Konrad Handrich, Sep 30 2024

Keywords

• nonn
• tabf

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.

Examples

			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;
...
		

References

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

Crossrefs

Cf. A000112, A022016, A022017, A342447.

Row sums: A133983.