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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

Table of n, a(n) for n=1..45.

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

Cf. A048793, A051185, A305843, A317752, A317755, A317757, A319077, A326031, A326910, A326911.

Cf. A318715, A319759, A319762, A319763, A319764.

Sequence in context: A044239 A044620 A209988 * A327147 A346898 A120534

Adjacent sequences:  A326909 A326910 A326911 * A326913 A326914 A326915

KEYWORD

nonn

AUTHOR

Gus Wiseman, Aug 04 2019

STATUS

approved

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Last modified May 20 01:04 EDT 2022. Contains 353847 sequences. (Running on oeis4.)