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A368600
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Number of ways to choose a set of n nonempty subsets of {1..n} such that it is not possible to choose a different element from each.
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16
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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The a(3) = 3 set-systems:
{{1},{2},{1,2}}
{{1},{3},{1,3}}
{{2},{3},{2,3}}
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MATHEMATICA
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Table[Length[Select[Subsets[Rest[Subsets[Range[n]]], {n}], Length[Select[Tuples[#], UnsameQ@@#&]]==0&]], {n, 0, 3}]
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PROG
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(Python)
from itertools import combinations, product, chain
from scipy.special import comb
def v(c):
for elements in product(*c):
if len(set(elements)) == len(elements):
return True
return False
def a(n):
if n == 0:
return 1
subsets = list(chain.from_iterable(combinations(range(1, n + 1), r) for r in range(1, n + 1)))
cs = combinations(subsets, n)
c = sum(1 for c in cs if v(c))
return c
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CROSSREFS
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Sets of n nonempty subsets of {1..n} are counted by A136556.
A059201 counts covering T_0 set-systems.
Cf. A003025, A088957, A133686, A334282, A355529, A355740, A367862, A367867, A367868, A367901, A368094, A368097.
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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