reviewed
reviewed
proposed
editing
Edge-connectivity of the set-system with BII-number n.
Elements of a set-system are sometimes called edges. The edge-connectivity of a set-system is the minimum number of edges that must be removed to result in a disconnected (or empty) set-system.
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]]]]]]]]];
edgeConn[y_]:=If[Length[csm[bpe/@y]]!=1, 0, Length[y]-Max@@Length/@Select[Union[Subsets[y]], Length[csm[bpe/@#]]!=1&]];
Table[edgeConn[bpe[n]], {n, 0, 100}]
approved
A binary index of n is any position of a 1 in its reversed binary digits. 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 finite set of finite nonempty sets has a different BII-number. For example, 18 has reversed binary digits (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.
proposed
editing
allocated for Gus Wiseman
allocated
approved