OFFSET
1,2
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 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 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.
EXAMPLE
The sequence of all set-systems with empty intersection together with their BII-numbers begins:
0: {}
3: {{1},{2}}
7: {{1},{2},{1,2}}
9: {{1},{3}}
10: {{2},{3}}
11: {{1},{2},{3}}
12: {{1,2},{3}}
13: {{1},{1,2},{3}}
14: {{2},{1,2},{3}}
15: {{1},{2},{1,2},{3}}
18: {{2},{1,3}}
19: {{1},{2},{1,3}}
22: {{2},{1,2},{1,3}}
23: {{1},{2},{1,2},{1,3}}
25: {{1},{3},{1,3}}
26: {{2},{3},{1,3}}
27: {{1},{2},{3},{1,3}}
28: {{1,2},{3},{1,3}}
29: {{1},{1,2},{3},{1,3}}
30: {{2},{1,2},{3},{1,3}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], #==0||Intersection@@bpe/@bpe[#]=={}&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 04 2019
STATUS
approved