login
A327145
Number of connected set-systems with n vertices and at least one bridge (spanning edge-connectivity 1).
11
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.
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.
Sequence in context: A158262 A300513 A089035 * A089516 A361217 A000573
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Aug 27 2019
STATUS
approved