The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326854 BII-numbers of T_0 (costrict), pairwise intersecting set-systems where every two vertices appear together in some edge (cointersecting). 5
 0, 1, 2, 5, 6, 8, 17, 24, 34, 40, 52, 69, 70, 81, 84, 85, 88, 98, 100, 102, 104, 112, 116, 120, 128, 257, 384, 514, 640, 772, 1029, 1030, 1281, 1284, 1285, 1408, 1538, 1540, 1542, 1664, 1792, 1796, 1920, 2056, 2176, 2320, 2592, 2880, 3120, 3152, 3168, 3184 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A set-system is a finite set of finite nonempty sets. Its elements are sometimes called edges. The dual of a set-system has, for each vertex, one edge consisting of the indices (or positions) of the edges containing that vertex. For example, the dual of {{1,2},{2,3}} is {{1},{1,2},{2}}. This sequence gives all BII-numbers (defined below) of pairwise intersecting set-systems whose dual is strict and pairwise intersecting. 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 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. LINKS EXAMPLE The sequence of all set-systems that are pairwise intersecting, cointersecting, and costrict, together with their BII-numbers, begins:     0: {}     1: {{1}}     2: {{2}}     5: {{1},{1,2}}     6: {{2},{1,2}}     8: {{3}}    17: {{1},{1,3}}    24: {{3},{1,3}}    34: {{2},{2,3}}    40: {{3},{2,3}}    52: {{1,2},{1,3},{2,3}}    69: {{1},{1,2},{1,2,3}}    70: {{2},{1,2},{1,2,3}}    81: {{1},{1,3},{1,2,3}}    84: {{1,2},{1,3},{1,2,3}}    85: {{1},{1,2},{1,3},{1,2,3}}    88: {{3},{1,3},{1,2,3}}    98: {{2},{2,3},{1,2,3}}   100: {{1,2},{2,3},{1,2,3}}   102: {{2},{1,2},{2,3},{1,2,3}} MATHEMATICA dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Select[Range[0, 10000], UnsameQ@@dual[bpe/@bpe[#]]&&stableQ[bpe/@bpe[#], Intersection[#1, #2]=={}&]&&stableQ[dual[bpe/@bpe[#]], Intersection[#1, #2]=={}&]&] CROSSREFS Equals the intersection of A326947, A326910, and A326853. These set-systems are counted by A319774 (covering). The non-T_0 version is A327061. Cf. A029931, A048793, A051185, A305843, A319765, A326031, A327037, A327038, A327041, A327052, A327053. Sequence in context: A191204 A191140 A271430 * A097685 A136369 A305511 Adjacent sequences:  A326851 A326852 A326853 * A326855 A326856 A326857 KEYWORD nonn AUTHOR Gus Wiseman, Aug 18 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 30 11:55 EDT 2020. Contains 337439 sequences. (Running on oeis4.)