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A327130 Number of set-systems covering n vertices with spanning edge-connectivity 2. 11
0, 0, 0, 32, 9552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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.

EXAMPLE

The a(3) = 32 set-systems:

{12}{13}{23}  {1}{12}{13}{23}  {1}{2}{12}{13}{23}  {1}{2}{3}{12}{13}{23}

{12}{13}{123} {2}{12}{13}{23}  {1}{3}{12}{13}{23}  {1}{2}{3}{12}{13}{123}

{12}{23}{123} {3}{12}{13}{23}  {2}{3}{12}{13}{23}  {1}{2}{3}{12}{23}{123}

{13}{23}{123} {1}{12}{13}{123} {1}{2}{12}{13}{123} {1}{2}{3}{13}{23}{123}

              {1}{12}{23}{123} {1}{2}{12}{23}{123}

              {1}{13}{23}{123} {1}{2}{13}{23}{123}

              {2}{12}{13}{123} {1}{3}{12}{13}{123}

              {2}{12}{23}{123} {1}{3}{12}{23}{123}

              {2}{13}{23}{123} {1}{3}{13}{23}{123}

              {3}{12}{13}{123} {2}{3}{12}{13}{123}

              {3}{12}{23}{123} {2}{3}{12}{23}{123}

              {3}{13}{23}{123} {2}{3}{13}{23}{123}

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], #]==2&]], {n, 0, 3}]

CROSSREFS

The BII-numbers of these set-systems are A327108.

Set-systems with spanning edge-connectivity 1 are A327145.

The restriction to simple graphs is A327146.

Cf. A003465, A323818, A327069, A327109, A327111, A327144.

Sequence in context: A139568 A139294 A227603 * A231035 A213813 A241369

Adjacent sequences:  A327127 A327128 A327129 * A327131 A327132 A327133

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 27 2019

STATUS

approved

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Last modified July 8 01:48 EDT 2020. Contains 335502 sequences. (Running on oeis4.)