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 A326947 BII-numbers of T_0 set-systems. 21
 0, 1, 2, 3, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 67, 69, 70, 71, 73, 74, 75, 77, 78 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The dual of a set-system has, for each vertex, one block consisting of the indices (or positions) of the blocks containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. The T_0 condition means that the dual is strict (no repeated edges). 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 T_0 set-systems together with their BII numbers begins:    0: {}    1: {{1}}    2: {{2}}    3: {{1},{2}}    5: {{1},{1,2}}    6: {{2},{1,2}}    7: {{1},{2},{1,2}}    8: {{3}}    9: {{1},{3}}   10: {{2},{3}}   11: {{1},{2},{3}}   13: {{1},{1,2},{3}}   14: {{2},{1,2},{3}}   15: {{1},{2},{1,2},{3}}   17: {{1},{1,3}}   19: {{1},{2},{1,3}}   20: {{1,2},{1,3}}   21: {{1},{1,2},{1,3}}   22: {{2},{1,2},{1,3}}   23: {{1},{2},{1,2},{1,3}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; TZQ[sys_]:=UnsameQ@@dual[sys]; Select[Range[0, 100], TZQ[bpe/@bpe[#]]&] CROSSREFS T_0 set-systems are counted by A326940, with unlabeled version A326946. Cf. A059201, A316978, A319559, A319564, A326939, A326941, A326949. Sequence in context: A047588 A213257 A039213 * A256450 A119605 A144146 Adjacent sequences:  A326944 A326945 A326946 * A326948 A326949 A326950 KEYWORD nonn AUTHOR Gus Wiseman, Aug 08 2019 STATUS approved

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Last modified February 18 00:37 EST 2020. Contains 332006 sequences. (Running on oeis4.)