
COMMENTS

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 setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem (finite set of finite nonempty sets) has a different BIInumber. 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 BIInumber of {{2},{1,3}} is 18. Elements of a setsystem are sometimes called edges.
The spanning edgeconnectivity of a setsystem is the minimum number of edges that must be removed (without removing incident vertices) to obtain a setsystem that is disconnected or covers fewer vertices.


EXAMPLE

The sequence of terms together with their corresponding setsystems begins:
0: {}
1: {{1}}
52: {{1,2},{1,3},{2,3}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
3952: {{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4}}
8052: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{1,2,3},{1,2,4},{1,3,4}}


CROSSREFS

The same for cutconnectivity is A327234.
The same for nonspanning edgeconnectivity is A002450.
The spanning edgeconnectivity of the setsystem with BIInumber n is A327144(n).
Cf. A000120, A048793, A070939, A323818, A326031, A326786, A326787, A327041, A327069, A327076, A327108, A327111, A327130, A327145.
Sequence in context: A044620 A209988 A326912 * A120534 A122166 A205221
Adjacent sequences: A327144 A327145 A327146 * A327148 A327149 A327150
