cp's OEIS Frontend

A367868 Number of labeled simple graphs covering n vertices and contradicting a strict version of the axiom of choice.

%I A367868 #12 Dec 30 2023 17:40:21
%S A367868 0,0,0,0,7,381,21853,1790135,250562543,66331467215,34507857686001,
%T A367868 35645472109753873,73356936892660012513,301275024409580265134121,
%U A367868 2471655539736293803311467943,40527712706903494712385171632959,1328579255614092966328511889576785109
%N A367868 Number of labeled simple graphs covering n vertices and contradicting a strict version of the axiom of choice.
%C A367868 The axiom of choice says that, given any set of nonempty sets Y, it is possible to choose a set containing an element from each. The strict version requires this set to have the same cardinality as Y, meaning no element is chosen more than once.
%H A367868 Andrew Howroyd, <a href="/A367868/b367868.txt">Table of n, a(n) for n = 0..50</a>
%F A367868 a(n) = A006129(n) - A367869(n). - _Andrew Howroyd_, Dec 30 2023
%e A367868 The a(4) = 7 graphs:
%e A367868   {{1,2},{1,3},{1,4},{2,3},{2,4}}
%e A367868   {{1,2},{1,3},{1,4},{2,3},{3,4}}
%e A367868   {{1,2},{1,3},{1,4},{2,4},{3,4}}
%e A367868   {{1,2},{1,3},{2,3},{2,4},{3,4}}
%e A367868   {{1,2},{1,4},{2,3},{2,4},{3,4}}
%e A367868   {{1,3},{1,4},{2,3},{2,4},{3,4}}
%e A367868   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
%t A367868 Table[Length[Select[Subsets[Subsets[Range[n],{2}]], Union@@#==Range[n]&&Select[Tuples[#], UnsameQ@@#&]=={}&]],{n,0,5}]
%Y A367868 The connected case is A140638, unlabeled A140636.
%Y A367868 The non-covering case is A367867.
%Y A367868 The complement is A367869, connected A129271, non-covering A133686.
%Y A367868 The version for set-systems is A367903, ranks A367907.
%Y A367868 A001187 counts connected graphs, A001349 unlabeled.
%Y A367868 A006125 counts graphs, A000088 unlabeled.
%Y A367868 A006129 counts covering graphs, A002494 unlabeled.
%Y A367868 A058891 counts set-systems (without singletons A016031), unlabeled A000612.
%Y A367868 A059201 counts covering T_0 set-systems, unlabeled A319637, ranks A326947.
%Y A367868 A143543 counts simple labeled graphs by number of connected components.
%Y A367868 Cf. A057500, A116508, A367769, A367770, A367863, A367901, A367902, A367904.
%K A367868 nonn
%O A367868 0,5
%A A367868 _Gus Wiseman_, Dec 08 2023
%E A367868 Terms a(7) and beyond from _Andrew Howroyd_, Dec 30 2023