cp's OEIS Frontend

A367902 Number of sets of nonempty subsets of {1..n} satisfying a strict version of the axiom of choice.

%I A367902 #11 Jul 25 2024 18:29:01
%S A367902 1,2,7,61,1771,187223,70038280,90111497503,397783376192189
%N A367902 Number of sets of nonempty subsets of {1..n} satisfying a strict version of the axiom of choice.
%C A367902 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 A367902 Wikipedia, <a href="https://en.wikipedia.org/wiki/Axiom_of_choice">Axiom of choice</a>.
%F A367902 a(n) = A370636(2^n-1). - _Alois P. Heinz_, Mar 09 2024
%e A367902 The a(2) = 7 set-systems:
%e A367902   {}
%e A367902   {{1}}
%e A367902   {{2}}
%e A367902   {{1,2}}
%e A367902   {{1},{2}}
%e A367902   {{1},{1,2}}
%e A367902   {{2},{1,2}}
%t A367902 Table[Length[Select[Subsets[Subsets[Range[n]]], Select[Tuples[#],UnsameQ@@#&]!={}&]],{n,0,3}]
%Y A367902 The version for simple graphs is A133686, covering A367869.
%Y A367902 The version without singletons is A367770.
%Y A367902 The complement allowing empty edges is A367901.
%Y A367902 The complement is A367903, without singletons A367769, ranks A367907.
%Y A367902 For a unique choice we have A367904, ranks A367908.
%Y A367902 These set-systems have ranks A367906.
%Y A367902 A000372 counts antichains, covering A006126, nonempty A014466.
%Y A367902 A003465 counts covering set-systems, unlabeled A055621.
%Y A367902 A058891 counts set-systems, unlabeled A000612.
%Y A367902 A059201 counts covering T_0 set-systems.
%Y A367902 A323818 counts covering connected set-systems.
%Y A367902 A326031 gives weight of the set-system with BII-number n.
%Y A367902 Cf. A007716, A083323, A092918, A102896, A283877, A306445, A355739, A355740, A367862, A367905, A370636.
%K A367902 nonn,more
%O A367902 0,2
%A A367902 _Gus Wiseman_, Dec 05 2023
%E A367902 a(6)-a(8) from _Christian Sievers_, Jul 25 2024