login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A327145 Number of connected set-systems with n vertices and at least one bridge (spanning edge-connectivity 1). 11
0, 1, 4, 56, 4640 (list; graph; refs; listen; history; text; internal format)
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 A000573 A070019

Adjacent sequences:  A327142 A327143 A327144 * A327146 A327147 A327148

KEYWORD

nonn,more

AUTHOR

Gus Wiseman, Aug 27 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified February 24 18:55 EST 2021. Contains 341584 sequences. (Running on oeis4.)