A327145 Number of connected set-systems with n vertices and at least one bridge (spanning edge-connectivity 1).

0, 1, 4, 56, 4640

Offset

0,3

Comments

A set-system is a finite set of finite nonempty sets. Elements of a set-system are sometimes called edges. The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a disconnected or empty set-system.

Links

Table of n, a(n) for n=0..4.

Mathematica

csm[s_]:=With[{c=Select[Tuples[Range[Length[s]], 2], And[OrderedQ[#], UnsameQ@@#, Length[Intersection@@s[[#]]]>0]&]}, If[c=={}, s, csm[Sort[Append[Delete[s, List/@c[[1]]], Union@@s[[c[[1]]]]]]]]];
spanEdgeConn[vts_, eds_]:=Length[eds]-Max@@Length/@Select[Subsets[eds], Union@@#!=vts||Length[csm[#]]!=1&];
Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], spanEdgeConn[Range[n], #]==1&]], {n, 0, 3}]

Crossrefs

The BII-numbers of these set-systems are A327111.

Set systems with non-spanning edge-connectivity 1 are A327196, with covering case A327129.

Set systems with spanning edge-connectivity 2 are A327130.

Cf. A003465, A323818, A327069, A327071, A327099, A327108, A327144.

Sequence in context: A158262 A300513 A089035 * A089516 A361217 A000573

Adjacent sequences: A327142 A327143 A327144 * A327146 A327147 A327148

Keyword

nonn,more

Author

Gus Wiseman, Aug 27 2019

Status

approved