login
A263857
Triangle read by rows: T(n,k) (n>=0, k>=n+1) is the number of posets with n elements and k antichains.
1
1, 1, 1, 1, 1, 2, 1, 0, 1, 1, 3, 3, 2, 3, 2, 0, 1, 0, 0, 0, 1, 1, 4, 6, 6, 9, 8, 7, 4, 5, 2, 2, 2, 3, 0, 2, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
0,6
COMMENTS
Row sums give A000112.
LINKS
FindStat - Combinatorial Statistic Finder, The number of antichains of a poset.
EXAMPLE
Triangle begins:
1,
1,
1,1,
1,2,1,0,1,
1,3,3,2,3,2,0,1,0,0,0,1,
1,4,6,6,9,8,7,4,5,2,2,2,3,0,2,0,0,0,1,0,0,0,0,0,0,0,1,
...
The two element poset with 2 incomparable elements x, y has 4 antichains: {}, {x}, {y}, and {x,y}. The two element poset with 2 comparable elements x, y has 3 antichains: {}, {x}, and {y}. So T(2,1) = 1 and T(2,2) = 1.
CROSSREFS
Cf. A000112.
Sequence in context: A083856 A081718 A290353 * A334895 A355262 A355576
KEYWORD
nonn,tabf
AUTHOR
Christian Stump, Oct 28 2015
STATUS
approved