A379712
Triangle read by rows: T(n,k) is the number of nonempty labeled antichains of subsets of [n] such that the largest subset is of size k.
Original entry on oeis.org
1, 1, 1, 1, 3, 1, 1, 7, 10, 1, 1, 15, 97, 53, 1, 1, 31, 1418, 5443, 686, 1, 1, 63, 40005, 3701128, 4043864, 43291, 1
Offset: 0
Triangle begins:
k=0 1 2 3 4 5
n=0 1;
n=1 1, 1;
n=2 1, 3, 1;
n=3 1, 7, 10, 1;
n=4 1, 15, 97, 53, 1;
n=5 1, 31, 1418, 5443, 686, 1;
...
T(3,0) = 1: {{}}.
T(3,1) = 7: {{1}}, {{2}}, {{3}}, {{1},{2}}, {{1},{3}}, {{2},{3}}, {{1},{2},{3}}.
T(3,2) = 10: {{1,2}}, {{1,3}}, {{2,3}}, {{1},{23}}, {{2},{13}}, {{3},{12}}, {{12},{13}}, {{12},{23}}, {{13},{23}}, {{12},{13},{23}}.
T(3,3) = 1: {{1,2,3}}.
A327363
Triangle read by rows where T(n,k) is the number of labeled simple graphs with n vertices and vertex-connectivity >= k.
Original entry on oeis.org
1, 1, 0, 2, 1, 0, 8, 4, 1, 0, 64, 38, 10, 1, 0, 1024, 728, 238, 26, 1, 0
Offset: 0
Triangle begins:
1
1 0
2 1 0
8 4 1 0
64 38 10 1 0
1024 728 238 26 1 0
Row-wise partial sums of
A327334 (vertex-connectivity exactly k).
-
vertConnSys[vts_,eds_]:=Min@@Length/@Select[Subsets[vts],Function[del,Length[del]==Length[vts]-1||csm[DeleteCases[DeleteCases[eds,Alternatives@@del,{2}],{}]]!={Complement[vts,del]}]];
Table[Length[Select[Subsets[Subsets[Range[n],{2}]],vertConnSys[Range[n],#]>=k&]],{n,0,4},{k,0,n}]
A327807
Triangle read by rows where T(n,k) is the number of unlabeled antichains of sets with n vertices and vertex-connectivity >= k.
Original entry on oeis.org
1, 2, 0, 4, 1, 0, 9, 3, 2, 0, 29, 14, 10, 6, 0, 209, 157, 128, 91, 54, 0
Offset: 0
Triangle begins:
1
2 0
4 1 0
9 3 2 0
29 14 10 6 0
209 157 128 91 54 0
Except for the first column, same as
A327358 (the covering case).
Showing 1-3 of 3 results.
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