cp's OEIS Frontend

A367901 Number of sets of subsets of {1..n} contradicting a strict version of the axiom of choice.

%I A367901 #13 Aug 01 2024 14:19:52
%S A367901 1,2,9,195,63765,4294780073,18446744073639513336,
%T A367901 340282366920938463463374607341656713953,
%U A367901 115792089237316195423570985008687907853269984665640564039457583610129753447747
%N A367901 Number of sets of subsets of {1..n} contradicting a strict version of the axiom of choice.
%C A367901 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 A367901 Wikipedia, <a href="https://en.wikipedia.org/wiki/Axiom_of_choice">Axiom of choice</a>.
%F A367901 a(n) = 2^2^n - A367902(n). - _Christian Sievers_, Aug 01 2024
%e A367901 The a(2) = 9 sets of sets:
%e A367901   {{}}
%e A367901   {{},{1}}
%e A367901   {{},{2}}
%e A367901   {{},{1,2}}
%e A367901   {{},{1},{2}}
%e A367901   {{},{1},{1,2}}
%e A367901   {{},{2},{1,2}}
%e A367901   {{1},{2},{1,2}}
%e A367901   {{},{1},{2},{1,2}}
%t A367901 Table[Length[Select[Subsets[Subsets[Range[n]]], Select[Tuples[#],UnsameQ@@#&]=={}&]],{n,0,3}]
%Y A367901 The version for simple graphs is A367867, covering A367868.
%Y A367901 The complement is counted by A367902, no singletons A367770, ranks A367906.
%Y A367901 The version without empty edges is A367903, ranks A367907.
%Y A367901 For a unique choice (instead of none) we have A367904, ranks A367908.
%Y A367901 A000372 counts antichains, covering A006126, nonempty A014466.
%Y A367901 A003465 counts covering set-systems, unlabeled A055621.
%Y A367901 A058891 counts set-systems, unlabeled A000612.
%Y A367901 A059201 counts covering T_0 set-systems.
%Y A367901 A323818 counts covering connected set-systems, unlabeled A323819.
%Y A367901 A326031 gives weight of the set-system with BII-number n.
%Y A367901 Cf. A007716, A083323, A092918, A102896, A283877, A306445, A355739, A355740, A367769, A367862, A367905.
%K A367901 nonn
%O A367901 0,2
%A A367901 _Gus Wiseman_, Dec 05 2023
%E A367901 a(5)-a(8) from _Christian Sievers_, Aug 01 2024