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 A329626 Smallest BII-number of an antichain with n edges. 4
 0, 1, 3, 11, 139, 820, 2868, 35636, 199476, 723764 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 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 set-system (finite set of finite nonempty sets of positive integers) 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. A set-system is an antichain if no edge is a proper subset of any other. LINKS EXAMPLE The sequence of terms together with their corresponding set-systems begins:        0: {}        1: {{1}}        3: {{1},{2}}       11: {{1},{2},{3}}      139: {{1},{2},{3},{4}}      820: {{1,2},{1,3},{2,3},{1,4},{2,4}}     2868: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4}}    35636: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{5}}   199476: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{1,5},{2,5}}   723764: {{1,2},{1,3},{2,3},{1,4},{2,4},{3,4},{1,5},{2,5},{3,5}} MATHEMATICA bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; stableQ[u_]:=!Apply[Or, Outer[#1=!=#2&&SubsetQ[#1, #2]&, u, u, 1], {0, 1}]; First/@GatherBy[Select[Range[0, 10000], stableQ[bpe/@bpe[#]]&], Length[bpe[#]]&] CROSSREFS The connected case is A329627. The intersecting case is A329628. BII-numbers of antichains are A326704. Antichain covers are A006126. Cf. A048143, A048793, A070939, A303362, A319837, A326031, A326750, A329555, A329560, A329561, A329625. Sequence in context: A121897 A067657 A063502 * A072639 A201000 A100459 Adjacent sequences:  A329623 A329624 A329625 * A329627 A329628 A329629 KEYWORD nonn,more AUTHOR Gus Wiseman, Nov 28 2019 STATUS approved

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Last modified June 2 06:13 EDT 2020. Contains 334767 sequences. (Running on oeis4.)