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Triangle read by rows: T(n,k) (n>=0, k>=n+1) is the number of posets with n elements and whose order polytope has k facets.
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%I #11 Oct 31 2015 14:41:09

%S 1,1,1,1,1,3,1,1,7,6,2,1,13,26,17,4,2,1,22,85,112,60,27,7,3,1

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

%C Row sums give A000112.

%C The order polytope of a poset P is given by all points in the unit cube [0,1]^P such that xp<xq for all p<q in P.

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000104">The number of facets in the order polytope of this poset</a>.

%H Richard Stanley, <a href="http://dedekind.mit.edu/~rstan/pubs/pubfiles/66.pdf">Two poset polytopes</a>, Discrete & Computational Geometry 1 (1986), DOI: 10.1007/BF02187680.

%e Triangle begins:

%e 1,

%e 1,

%e 1,1,

%e 1,3,1,

%e 1,7,6,2,

%e 1,13,26,17,4,2,

%e 1,22,85,112,60,27,7,3,1,

%e ...

%Y Cf. A000112.

%K nonn,tabf,more

%O 0,6

%A _Christian Stump_, Oct 28 2015