A326788 - OEIS

A326788

BII-numbers of simple labeled graphs.

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

(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.

Also numbers whose binary indices all belong to A018900.

LINKS

Table of n, a(n) for n=1..50.

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

Cf. A000120, A006125, A006129, A018900, A048793, A062880, A070939, A309356 (same for MM-numbers), A322551, A326031, A326702.

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

Adjacent sequences: A326785 A326786 A326787 * A326789 A326790 A326791

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 25 2019

STATUS

approved