cp's OEIS Frontend

A326912 BII-numbers of pairwise intersecting set-systems with empty intersection.

%I A326912 #5 Aug 05 2019 07:37:04
%S A326912 0,52,116,772,832,836,1072,1076,1136,1140,1796,1856,1860,2320,2368,
%T A326912 2384,2592,2624,2656,2880,3088,3104,3120,3136,3152,3168,3184,3344,
%U A326912 3392,3408,3616,3648,3680,3904,4132,4148,4196,4212,4612,4640,4644,4672,4676,4704,4708
%N A326912 BII-numbers of pairwise intersecting set-systems with empty intersection.
%C A326912 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 A326912 The sequence of all pairwise intersecting set-systems with empty intersection, together with their BII-numbers, begins:
%e A326912      0: {}
%e A326912     52: {{1,2},{1,3},{2,3}}
%e A326912    116: {{1,2},{1,3},{2,3},{1,2,3}}
%e A326912    772: {{1,2},{1,4},{2,4}}
%e A326912    832: {{1,2,3},{1,4},{2,4}}
%e A326912    836: {{1,2},{1,2,3},{1,4},{2,4}}
%e A326912   1072: {{1,3},{2,3},{1,2,4}}
%e A326912   1076: {{1,2},{1,3},{2,3},{1,2,4}}
%e A326912   1136: {{1,3},{2,3},{1,2,3},{1,2,4}}
%e A326912   1140: {{1,2},{1,3},{2,3},{1,2,3},{1,2,4}}
%e A326912   1796: {{1,2},{1,4},{2,4},{1,2,4}}
%e A326912   1856: {{1,2,3},{1,4},{2,4},{1,2,4}}
%e A326912   1860: {{1,2},{1,2,3},{1,4},{2,4},{1,2,4}}
%e A326912   2320: {{1,3},{1,4},{3,4}}
%e A326912   2368: {{1,2,3},{1,4},{3,4}}
%e A326912   2384: {{1,3},{1,2,3},{1,4},{3,4}}
%e A326912   2592: {{2,3},{2,4},{3,4}}
%e A326912   2624: {{1,2,3},{2,4},{3,4}}
%e A326912   2656: {{2,3},{1,2,3},{2,4},{3,4}}
%e A326912   2880: {{1,2,3},{1,4},{2,4},{3,4}}
%t A326912 bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n,2]],1];
%t A326912 Select[Range[0,1000],(#==0||Intersection@@bpe/@bpe[#]=={})&&stableQ[bpe/@bpe[#],Intersection[#1,#2]=={}&]&]
%Y A326912 Cf. A048793, A051185, A305843, A317752, A317755, A317757, A319077, A326031, A326910, A326911.
%Y A326912 Cf. A318715, A319759, A319762, A319763, A319764.
%K A326912 nonn
%O A326912 1,2
%A A326912 _Gus Wiseman_, Aug 04 2019