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A326788
BII-numbers of simple labeled graphs.
13
0, 4, 16, 20, 32, 36, 48, 52, 256, 260, 272, 276, 288, 292, 304, 308, 512, 516, 528, 532, 544, 548, 560, 564, 768, 772, 784, 788, 800, 804, 816, 820, 2048, 2052, 2064, 2068, 2080, 2084, 2096, 2100, 2304, 2308, 2320, 2324, 2336, 2340, 2352, 2356, 2560, 2564
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.
Also numbers whose binary indices all belong to A018900.
EXAMPLE
The sequence of all simple labeled graphs together with their BII-numbers begins:
0: {}
4: {{1,2}}
16: {{1,3}}
20: {{1,2},{1,3}}
32: {{2,3}}
36: {{1,2},{2,3}}
48: {{1,3},{2,3}}
52: {{1,2},{1,3},{2,3}}
256: {{1,4}}
260: {{1,2},{1,4}}
272: {{1,3},{1,4}}
276: {{1,2},{1,3},{1,4}}
288: {{2,3},{1,4}}
292: {{1,2},{2,3},{1,4}}
304: {{1,3},{2,3},{1,4}}
308: {{1,2},{1,3},{2,3},{1,4}}
512: {{2,4}}
516: {{1,2},{2,4}}
528: {{1,3},{2,4}}
532: {{1,2},{1,3},{2,4}}
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Select[Range[0, 100], SameQ[2, ##]&@@Length/@bpe/@bpe[#]&]
CROSSREFS
Other BII-numbers: A309314 (hyperforests), A326701 (set partitions), A326703 (chains), A326704 (antichains), A326749 (connected), A326750 (clutters), A326751 (blobs), A326752 (hypertrees), A326754 (covers).
Sequence in context: A071966 A349521 A326781 * A039943 A193996 A232400
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 25 2019
STATUS
approved