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 A327052 Number of T_0 (costrict) set-systems covering a subset of {1..n} where every two covered vertices appear together in some edge (cointersecting). 8
 1, 2, 6, 75, 24981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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 counts set-systems whose dual is strict and pairwise intersecting. LINKS FORMULA Binomial transform of A327053. EXAMPLE The a(0) = 1 through a(2) = 6 set-systems: {} {} {} {{1}} {{1}} {{2}} {{1},{1,2}} {{2},{1,2}} {{1},{2},{1,2}} MATHEMATICA dual[eds_]:=Table[First/@Position[eds, x], {x, Union@@eds}]; stableQ[u_, Q_]:=!Apply[Or, Outer[#1=!=#2&&Q[#1, #2]&, u, u, 1], {0, 1}]; Table[Length[Select[Subsets[Subsets[Range[n], {1, n}]], UnsameQ@@dual[#]&&stableQ[dual[#], Intersection[#1, #2]=={}&]&]], {n, 0, 3}] CROSSREFS The unlabeled multiset partition version is A319760. The non-T_0 version is A327039. The covering case is A327053. Cf. A051185, A319752, A319774, A327038, A327040. Sequence in context: A065410 A000721 A262279 * A231508 A136306 A274825 Adjacent sequences: A327049 A327050 A327051 * A327053 A327054 A327055 KEYWORD nonn,more AUTHOR Gus Wiseman, Aug 18 2019 STATUS approved

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Last modified January 30 16:07 EST 2023. Contains 359945 sequences. (Running on oeis4.)