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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

%I #9 Oct 31 2015 14:38:29

%S 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,

%T 0,2,0,0,0,1,0,0,0,0,0,0,0,1

%N Triangle read by rows: T(n,k) (n>=0, k>=n+1) is the number of posets with n elements and k antichains.

%C Row sums give A000112.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000070">The number of antichains of a poset</a>.

%e Triangle begins:

%e 1,

%e 1,

%e 1,1,

%e 1,2,1,0,1,

%e 1,3,3,2,3,2,0,1,0,0,0,1,

%e 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,

%e ...

%e 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.

%Y Cf. A000112.

%K nonn,tabf

%O 0,6

%A _Christian Stump_, Oct 28 2015

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Last modified March 28 17:42 EDT 2024. Contains 371254 sequences. (Running on oeis4.)