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%I #6 Sep 01 2019 22:03:52
%S 0,1,52,116,3952,8052
%N Smallest BII-number of a set-system with spanning edge-connectivity n.
%C 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.
%C 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 set-system that is disconnected or covers fewer vertices.
%e The sequence of terms together with their corresponding set-systems begins:
%e 0: {}
%e 1: {{1}}
%e 52: {{1,2},{1,3},{2,3}}
%e 116: {{1,2},{1,3},{2,3},{1,2,3}}
%e 3952: {{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4}}
%e 8052: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4}}
%Y The same for cut-connectivity is A327234.
%Y The same for non-spanning edge-connectivity is A002450.
%Y The spanning edge-connectivity of the set-system with BII-number n is A327144(n).
%Y Cf. A000120, A048793, A070939, A323818, A326031, A326786, A326787, A327041, A327069, A327076, A327108, A327111, A327130, A327145.
%K nonn,more
%O 0,3
%A _Gus Wiseman_, Sep 01 2019
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