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A326912 BII-numbers of pairwise intersecting set-systems with empty intersection. 11
0, 52, 116, 772, 832, 836, 1072, 1076, 1136, 1140, 1796, 1856, 1860, 2320, 2368, 2384, 2592, 2624, 2656, 2880, 3088, 3104, 3120, 3136, 3152, 3168, 3184, 3344, 3392, 3408, 3616, 3648, 3680, 3904, 4132, 4148, 4196, 4212, 4612, 4640, 4644, 4672, 4676, 4704, 4708 (list; graph; refs; listen; history; text; internal format)
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.
LINKS
EXAMPLE
The sequence of all pairwise intersecting set-systems with empty intersection, together with their BII-numbers, begins:
0: {}
52: {{1,2},{1,3},{2,3}}
116: {{1,2},{1,3},{2,3},{1,2,3}}
772: {{1,2},{1,4},{2,4}}
832: {{1,2,3},{1,4},{2,4}}
836: {{1,2},{1,2,3},{1,4},{2,4}}
1072: {{1,3},{2,3},{1,2,4}}
1076: {{1,2},{1,3},{2,3},{1,2,4}}
1136: {{1,3},{2,3},{1,2,3},{1,2,4}}
1140: {{1,2},{1,3},{2,3},{1,2,3},{1,2,4}}
1796: {{1,2},{1,4},{2,4},{1,2,4}}
1856: {{1,2,3},{1,4},{2,4},{1,2,4}}
1860: {{1,2},{1,2,3},{1,4},{2,4},{1,2,4}}
2320: {{1,3},{1,4},{3,4}}
2368: {{1,2,3},{1,4},{3,4}}
2384: {{1,3},{1,2,3},{1,4},{3,4}}
2592: {{2,3},{2,4},{3,4}}
2624: {{1,2,3},{2,4},{3,4}}
2656: {{2,3},{1,2,3},{2,4},{3,4}}
2880: {{1,2,3},{1,4},{2,4},{3,4}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 1000], (#==0||Intersection@@bpe/@bpe[#]=={})&&stableQ[bpe/@bpe[#], Intersection[#1, #2]=={}&]&]
CROSSREFS
Sequence in context: A044239 A044620 A209988 * A327147 A346898 A120534
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 04 2019
STATUS
approved

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Last modified March 28 09:04 EDT 2024. Contains 371240 sequences. (Running on oeis4.)