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 A326905 BII-numbers of set-systems (without {}) closed under intersection. 2
 0, 1, 2, 4, 5, 6, 8, 16, 17, 21, 24, 32, 34, 38, 40, 56, 64, 65, 66, 68, 69, 70, 72, 80, 81, 85, 88, 96, 98, 102, 104, 120, 128, 256, 257, 261, 273, 277, 321, 325, 337, 341, 384, 512, 514, 518, 546, 550, 578, 582, 610, 614, 640, 896, 1024, 1025, 1026, 1028 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 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 set-systems closed under intersection together with their BII-numbers begins: 0: {} 1: {{1}} 2: {{2}} 4: {{1,2}} 5: {{1},{1,2}} 6: {{2},{1,2}} 8: {{3}} 16: {{1,3}} 17: {{1},{1,3}} 21: {{1},{1,2},{1,3}} 24: {{3},{1,3}} 32: {{2,3}} 34: {{2},{2,3}} 38: {{2},{1,2},{2,3}} 40: {{3},{2,3}} 56: {{3},{1,3},{2,3}} 64: {{1,2,3}} 65: {{1},{1,2,3}} 66: {{2},{1,2,3}} 68: {{1,2},{1,2,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; Select[Range[0, 100], SubsetQ[bpe/@bpe[#], Intersection@@@Tuples[bpe/@bpe[#], 2]]&] CROSSREFS The case with union instead of intersection is A326875. The case closed under union and intersection is A326913. Set-systems closed under intersection and containing the vertex set are A326903. Set-systems closed under intersection are A326901, with unlabeled version A326904. Cf. A006058, A102895, A102898, A326866, A326876, A326878, A326882, A326900, A326902. Sequence in context: A176654 A185867 A326910 * A327061 A326913 A326703 Adjacent sequences: A326902 A326903 A326904 * A326906 A326907 A326908 KEYWORD nonn AUTHOR Gus Wiseman, Aug 04 2019 STATUS approved

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Last modified March 31 17:28 EDT 2023. Contains 361668 sequences. (Running on oeis4.)