%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