cp's OEIS Frontend

A326911 BII-numbers of set-systems with empty intersection.

%I A326911 #5 Aug 05 2019 07:36:57
%S A326911 0,3,7,9,10,11,12,13,14,15,18,19,22,23,25,26,27,28,29,30,31,33,35,37,
%T A326911 39,41,42,43,44,45,46,47,49,50,51,52,53,54,55,57,58,59,60,61,62,63,67,
%U A326911 71,73,74,75,76,77,78,79,82,83,86,87,89,90,91,92,93,94,95
%N A326911 BII-numbers of set-systems with empty intersection.
%C A326911 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.
%e A326911 The sequence of all set-systems with empty intersection together with their BII-numbers begins:
%e A326911    0: {}
%e A326911    3: {{1},{2}}
%e A326911    7: {{1},{2},{1,2}}
%e A326911    9: {{1},{3}}
%e A326911   10: {{2},{3}}
%e A326911   11: {{1},{2},{3}}
%e A326911   12: {{1,2},{3}}
%e A326911   13: {{1},{1,2},{3}}
%e A326911   14: {{2},{1,2},{3}}
%e A326911   15: {{1},{2},{1,2},{3}}
%e A326911   18: {{2},{1,3}}
%e A326911   19: {{1},{2},{1,3}}
%e A326911   22: {{2},{1,2},{1,3}}
%e A326911   23: {{1},{2},{1,2},{1,3}}
%e A326911   25: {{1},{3},{1,3}}
%e A326911   26: {{2},{3},{1,3}}
%e A326911   27: {{1},{2},{3},{1,3}}
%e A326911   28: {{1,2},{3},{1,3}}
%e A326911   29: {{1},{1,2},{3},{1,3}}
%e A326911   30: {{2},{1,2},{3},{1,3}}
%t A326911 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A326911 Select[Range[0,100],#==0||Intersection@@bpe/@bpe[#]=={}&]
%Y A326911 Cf. A048793, A051185, A305843, A317752, A317755, A317757, A319077, A326031, A326910, A326912.
%K A326911 nonn
%O A326911 1,2
%A A326911 _Gus Wiseman_, Aug 04 2019