cp's OEIS Frontend

A367769 Number of finite sets of nonempty non-singleton subsets of {1..n} contradicting a strict version of the axiom of choice.

%I A367769 #16 Jul 28 2024 12:30:57
%S A367769 0,0,0,1,1490,67027582,144115188036455750,
%T A367769 1329227995784915872903806998967001298,
%U A367769 226156424291633194186662080095093570025917938800079226639565284090686126876
%N A367769 Number of finite sets of nonempty non-singleton subsets of {1..n} contradicting a strict version of the axiom of choice.
%C A367769 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 A367769 Includes all set-systems with more edges than covered vertices, but this condition is not sufficient.
%H A367769 Wikipedia, <a href="https://en.wikipedia.org/wiki/Axiom_of_choice">Axiom of choice</a>.
%F A367769 a(n) = 2^(2^n-n-1) - A367770(n) = A016031(n+1) - A367770(n). - _Christian Sievers_, Jul 28 2024
%e A367769 The a(3) = 1 set-system is: {{1,2},{1,3},{2,3},{1,2,3}}.
%t A367769 Table[Length[Select[Subsets[Select[Subsets[Range[n]], Length[#]>1&]], Select[Tuples[#], UnsameQ@@#&]=={}&]], {n,0,3}]
%Y A367769 Set-systems without singletons are counted by A016031, covering A323816.
%Y A367769 The complement is A367770, with singletons allowed A367902 (ranks A367906).
%Y A367769 The version for simple graphs is A367867, covering A367868.
%Y A367769 The version allowing singletons and empty edges is A367901.
%Y A367769 The version allowing singletons is A367903, ranks A367907.
%Y A367769 A000372 counts antichains, covering A006126, nonempty A014466.
%Y A367769 A003465 counts covering set-systems, unlabeled A055621.
%Y A367769 A058891 counts set-systems, unlabeled A000612.
%Y A367769 A059201 counts covering T_0 set-systems.
%Y A367769 A323818 counts covering connected set-systems.
%Y A367769 Cf. A007716, A092918, A102896, A283877, A306445, A326031, A355739, A355740, A355741, A367904, A367905.
%K A367769 nonn,more
%O A367769 0,5
%A A367769 _Gus Wiseman_, Dec 05 2023
%E A367769 a(6)-a(8) from _Christian Sievers_, Jul 28 2024