

A368596


Number of nelement sets of singletons or pairs of distinct elements of {1..n}, or loop graphs with n edges, such that it is not possible to choose a different element from each.


22



0, 0, 0, 3, 66, 1380, 31460, 800625, 22758918, 718821852, 25057509036, 957657379437, 39878893266795, 1799220308202603, 87502582432459584, 4566246347310609247, 254625879822078742956, 15115640124974801925030, 952050565540607423524658, 63425827673509972464868323
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OFFSET

0,4


COMMENTS

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.


LINKS



EXAMPLE

The a(3) = 3 setsystems:
{{1},{2},{1,2}}
{{1},{3},{1,3}}
{{2},{3},{2,3}}


MATHEMATICA

Table[Length[Select[Subsets[Subsets[Range[n], {1, 2}], {n}], Length[Select[Tuples[#], UnsameQ@@#&]]==0&]], {n, 0, 5}]


CROSSREFS

The version without the choice condition is A014068, covering A368597.
The complement appears to be A333331.
For covering pairs we have A367868.
Allowing edges of any positive size gives A368600, any length A367903.
A000085 counts set partitions into singletons or pairs.
A100861 counts set partitions into singletons or pairs by number of pairs.
A111924 counts set partitions into singletons or pairs by length.
Cf. A000272, A000666, A057500, A129271, A133686, A367769, A367863, A367867, A367869, A367901, A367907, A368097, A369199.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



