A318128
Number of set-systems (finite sets of finite nonempty sets) with union {1,2,...,n} and intersection {}.
Original entry on oeis.org
1, 0, 2, 84, 31478, 2147000136, 9223371998203475474, 170141183460469231537996491257596836636, 57896044618658097711785492504343953922551603929769020459976077632195066756398
Offset: 0
The a(2) = 2 set-systems are {{1},{2}}, and {{1},{2},{1,2}}.
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Table[Length[Select[Subsets[Rest[Subsets[Range[n]]]],And[Union@@#===Range[n],Intersection@@#=={}]&]],{n,4}]
A318129
Number of sets of nonempty subsets of {1,...,n} with intersection {}.
Original entry on oeis.org
1, 1, 3, 91, 31827, 2147158387, 9223372011085950171, 170141183460469231602560095290109272523, 57896044618658097711785492504343953923912733397452774312538303978325772978595
Offset: 0
The a(2) = 3 sets of sets are {}, {{1},{2}}, {{1},{2},{1,2}}.
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Table[Length[Select[Subsets[Rest[Subsets[Range[n]]]],Or[#=={},Intersection@@#=={}]&]],{n,0,4}]
A318131
Number of non-isomorphic sets of finite (possibly empty) sets with union {1,2,...,n} and intersection {}.
Original entry on oeis.org
1, 1, 6, 60, 3836, 37325360, 25626412263611792, 67516342973185974276922865448446208, 2871827610052485009904013737758920847534777143951264797898686184985092096
Offset: 0
Non-isomorphic representatives of the a(2) = 6 sets of sets:
{{1},{2}}
{{},{1,2}}
{{},{1},{2}}
{{},{1},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
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sysnorm[m_]:=If[Union@@m!=Range[Max@@Flatten[m]],sysnorm[m/.Rule@@@Table[{(Union@@m)[[i]],i},{i,Length[Union@@m]}]],First[Sort[sysnorm[m,1]]]];sysnorm[m_,aft_]:=If[Length[Union@@m]<=aft,{m},With[{mx=Table[Count[m,i,{2}],{i,Select[Union@@m,#>=aft&]}]},Union@@(sysnorm[#,aft+1]&/@Union[Table[Map[Sort,m/.{par+aft-1->aft,aft->par+aft-1},{0,1}],{par,First/@Position[mx,Max[mx]]}]])]];
Table[Length[Union[sysnorm/@Select[Subsets[Subsets[Range[n]]],And[Union@@#===Range[n],Intersection@@#=={}]&]]],{n,4}]
A318130
Number of sets of subsets of {1,...,n} with intersection {}.
Original entry on oeis.org
2, 3, 11, 219, 64595, 4294642035, 18446744047940725979, 340282366920938463334247399005993378251, 115792089237316195423570985008687907850547725730273056332267095982282337798563
Offset: 0
The a(2) = 11 sets of sets:
{}
{{}}
{{},{1}}
{{},{2}}
{{1},{2}}
{{},{1,2}}
{{},{1},{2}}
{{},{1},{1,2}}
{{},{2},{1,2}}
{{1},{2},{1,2}}
{{},{1},{2},{1,2}}
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Table[Length[Select[Subsets[Subsets[Range[n]]],Or[#=={},Intersection@@#=={}]&]],{n,0,4}]
Showing 1-4 of 4 results.