cp's OEIS Frontend

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.

%I A376633 #6 Sep 30 2024 12:54:02
%S A376633 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,
%T A376633 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,
%U A376633 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
%N 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.
%C A376633 Posets whose Hasse diagram looks the same if it is turned upside down.
%C A376633 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.
%D A376633 R. P. Stanley, Enumerative Combinatorics I, 2nd. ed., pp. 277.
%e A376633 The table starts:
%e A376633 1 ;
%e A376633 1 1 ;
%e A376633 1 1 1 ;
%e A376633 1 1 2 2 2 ;
%e A376633 1 1 2 3 5 2 1 ;
%e A376633 1 1 2 4 9 11 12 5 4 1 ;
%e A376633 1 1 2 4 10 16 26 22 21 10 5 0 1 ;
%e A376633 1 1 2 4 11 20 44 65 98 86 79 41 25 8 4 2 2 ;
%e A376633 1 1 2 4 11 21 51 92 175 220 276 237 208 103 67 25 18 5 3 0 1 ;
%e A376633 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;
%e A376633 ...
%Y A376633 Cf. A000112, A022016, A022017, A342447.
%Y A376633 Row sums: A133983.
%K A376633 nonn,tabf
%O A376633 1,9
%A A376633 Rico Zöllner and _Konrad Handrich_, Sep 30 2024