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

1, 0, 1, 9, 315, 64880

Offset: 0

Author

Gus Wiseman, Aug 02 2018

Keywords

• nonn
• more

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.

Examples

			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}}}
		

Links

• 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.

Crossrefs

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