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 A327109 BII-numbers of set-systems with spanning edge-connectivity >= 2. 13
 52, 53, 54, 55, 60, 61, 62, 63, 84, 85, 86, 87, 92, 93, 94, 95, 100, 101, 102, 103, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 772, 773, 774, 775, 816, 817, 818, 819, 820, 821, 822, 823, 824, 825, 826 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Differs from A327108 in having 116, 117, 118, 119, 124, 125, 126, 127, ... A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every set-system (finite set of finite nonempty sets) has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. 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 EXAMPLE The sequence of all set-systems with spanning edge-connectivity >= 2 together with their BII-numbers begins:    52: {{1,2},{1,3},{2,3}}    53: {{1},{1,2},{1,3},{2,3}}    54: {{2},{1,2},{1,3},{2,3}}    55: {{1},{2},{1,2},{1,3},{2,3}}    60: {{1,2},{3},{1,3},{2,3}}    61: {{1},{1,2},{3},{1,3},{2,3}}    62: {{2},{1,2},{3},{1,3},{2,3}}    63: {{1},{2},{1,2},{3},{1,3},{2,3}}    84: {{1,2},{1,3},{1,2,3}}    85: {{1},{1,2},{1,3},{1,2,3}}    86: {{2},{1,2},{1,3},{1,2,3}}    87: {{1},{2},{1,2},{1,3},{1,2,3}}    92: {{1,2},{3},{1,3},{1,2,3}}    93: {{1},{1,2},{3},{1,3},{1,2,3}}    94: {{2},{1,2},{3},{1,3},{1,2,3}}    95: {{1},{2},{1,2},{3},{1,3},{1,2,3}}   100: {{1,2},{2,3},{1,2,3}}   101: {{1},{1,2},{2,3},{1,2,3}}   102: {{2},{1,2},{2,3},{1,2,3}}   103: {{1},{2},{1,2},{2,3},{1,2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; 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&]; Select[Range[0, 1000], spanEdgeConn[Union@@bpe/@bpe[#], bpe/@bpe[#]]>=2&] CROSSREFS Positions of terms >= 2 in  A327144. Graphs with spanning edge-connectivity >= 2 are counted by A095983. Graphs with spanning edge-connectivity 2 are counted by A327146. Set-systems with spanning edge-connectivity 2 are counted by A327130. BII-numbers for non-spanning edge-connectivity 2 are A327097. BII-numbers for non-spanning edge-connectivity >= 2 are A327102. BII-numbers for spanning edge-connectivity 2 are A327108. BII-numbers for spanning edge-connectivity 1 are A327111. Cf. A326749, A326753, A326787, A327041, A327069, A327071, A327075. Sequence in context: A252713 A249404 A327374 * A327108 A295156 A181461 Adjacent sequences:  A327106 A327107 A327108 * A327110 A327111 A327112 KEYWORD nonn AUTHOR Gus Wiseman, Aug 23 2019 STATUS approved

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Last modified May 9 04:17 EDT 2021. Contains 343685 sequences. (Running on oeis4.)