A263861 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.

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

Offset

0,6

Comments

Row sums give A000112.

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.

Links

Table of n, a(n) for n=0..25.

FindStat - Combinatorial Statistic Finder, The number of facets in the order polytope of this poset.

Richard Stanley, Two poset polytopes, Discrete & Computational Geometry 1 (1986), DOI: 10.1007/BF02187680.

Example

Triangle begins:
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,
...

Crossrefs

Cf. A000112.

Sequence in context: A185982 A263858 A263862 * A357940 A133800 A146900

Adjacent sequences: A263858 A263859 A263860 * A263862 A263863 A263864

Keyword

nonn,tabf,more

Author

Christian Stump, Oct 28 2015

Status

approved