A317634 Number of caps (also clutter partitions) of clutters (connected antichains) spanning n vertices.

1, 0, 1, 9, 315, 64880

Offset

0,4

Comments

A kernel of a clutter is the restriction of the edge set to all edges contained within some connected vertex set. A clutter partition is a set partition of the edge set using kernels.

Links

Table of n, a(n) for n=0..5.

Gus Wiseman, Every Clutter Is a Tree of Blobs, The Mathematica Journal, Vol. 19, 2017.

Gus Wiseman, All clutter partitions of non-isomorphic clutters on 4 vertices.

Example

The a(3) = 9 clutter partitions:
  {{{1,2,3}}}
  {{{1,3},{2,3}}}
  {{{1,2},{2,3}}}
  {{{1,2},{1,3}}}
  {{{1,3}},{{2,3}}}
  {{{1,2}},{{2,3}}}
  {{{1,2}},{{1,3}}}
  {{{1,2},{1,3},{2,3}}}
  {{{1,2}},{{1,3}},{{2,3}}}

Crossrefs

Cf. A001187, A030019, A048143, A275307, A286520,, A293510, A304717, A317631, A317632, A317635.

Sequence in context: A217145 A266835 A288324 * A198401 A135609 A349287

Adjacent sequences: A317631 A317632 A317633 * A317635 A317636 A317637

Keyword

nonn,more

Author

Gus Wiseman, Aug 02 2018

Status

approved