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A317634 Number of caps (also clutter partitions) of clutters (connected antichains) spanning n vertices. 11

%I #7 Aug 03 2018 08:16:31

%S 1,0,1,9,315,64880

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

%C 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.

%H Gus Wiseman, <a href="http://www.mathematica-journal.com/2017/12/every-clutter-is-a-tree-of-blobs/">Every Clutter Is a Tree of Blobs</a>, The Mathematica Journal, Vol. 19, 2017.

%H Gus Wiseman, <a href="/A317634/a317634.png">All clutter partitions of non-isomorphic clutters on 4 vertices.</a>

%e The a(3) = 9 clutter partitions:

%e {{{1,2,3}}}

%e {{{1,3},{2,3}}}

%e {{{1,2},{2,3}}}

%e {{{1,2},{1,3}}}

%e {{{1,3}},{{2,3}}}

%e {{{1,2}},{{2,3}}}

%e {{{1,2}},{{1,3}}}

%e {{{1,2},{1,3},{2,3}}}

%e {{{1,2}},{{1,3}},{{2,3}}}

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

%K nonn,more

%O 0,4

%A _Gus Wiseman_, Aug 02 2018

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)