cp's OEIS Frontend

A367867 Number of labeled simple graphs with n vertices contradicting a strict version of the axiom of choice.

%I A367867 #11 Dec 30 2023 17:36:24
%S A367867 0,0,0,0,7,416,24244,1951352,265517333,68652859502,35182667175398,
%T A367867 36028748718835272,73786974794973865449,302231454853009287213496,
%U A367867 2475880078568912926825399800,40564819207303268441662426947840,1329227995784915869870199216532048487
%N A367867 Number of labeled simple graphs with n vertices contradicting a strict version of the axiom of choice.
%C A367867 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.
%C A367867 In the connected case, these are just graphs with more than one cycle.
%H A367867 Andrew Howroyd, <a href="/A367867/b367867.txt">Table of n, a(n) for n = 0..50</a>
%F A367867 a(n) = A006125(n) - A133686(n). - _Andrew Howroyd_, Dec 30 2023
%e A367867 Non-isomorphic representatives of the a(4) = 7 graphs:
%e A367867   {{1,2},{1,3},{1,4},{2,3},{2,4}}
%e A367867   {{1,2},{1,3},{1,4},{2,3},{2,4},{3,4}}
%t A367867 Table[Length[Select[Subsets[Subsets[Range[n],{2}]], Select[Tuples[#],UnsameQ@@#&]=={}&]],{n,0,5}]
%Y A367867 The complement is A133686, connected A129271, covering A367869.
%Y A367867 The connected case is A140638 (graphs with more than one cycle).
%Y A367867 The covering case is A367868.
%Y A367867 For set-systems we have A367903, ranks A367907.
%Y A367867 A001187 counts connected graphs, A001349 unlabeled.
%Y A367867 A006125 counts graphs, A000088 unlabeled.
%Y A367867 A006129 counts covering graphs, A002494 unlabeled.
%Y A367867 A058891 counts set-systems, unlabeled A000612, without singletons A016031.
%Y A367867 A059201 counts covering T_0 set-systems, unlabeled A319637, ranks A326947.
%Y A367867 A143543 counts simple labeled graphs by number of connected components.
%Y A367867 Cf. A057500, A116508, A326754, A355739, A355740, A367769, A367770, A367863, A367901, A367902, A367904.
%K A367867 nonn
%O A367867 0,5
%A A367867 _Gus Wiseman_, Dec 07 2023
%E A367867 Terms a(7) and beyond from _Andrew Howroyd_, Dec 30 2023