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A330231
Number of distinct set-systems that can be obtained by permuting the vertices of the set-system with BII-number n.
13
1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 3, 6, 6, 3, 1, 2, 3, 6, 3, 3, 6, 6, 2, 1, 6, 3, 6, 6, 3, 3, 1, 3, 2, 6, 3, 6, 3, 6, 2, 6, 1, 3, 6, 3, 6, 3, 3, 6, 6, 3, 1, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 1, 1, 3, 3, 3, 3, 6, 6, 3, 3, 3, 3, 1, 3, 6, 6, 3, 3, 6, 3, 6, 3, 3, 6
OFFSET
0,6
COMMENTS
A set-system is a finite set of finite nonempty sets.
A binary index of n is any position of a 1 in its reversed binary expansion. The binary indices of n are row n of A048793. We define the set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every set-system has a different BII-number. For example, 18 has reversed binary expansion (0,1,0,0,1), and since the binary indices of 2 and 5 are {2} and {1,3} respectively, the BII-number of {{2},{1,3}} is 18. Elements of a set-system are sometimes called edges.
FORMULA
a(n) is a divisor of A326702(n)!.
EXAMPLE
30 is the MM-number of {{2},{3},{1,2},{1,3}}, with vertex permutations
{{1},{2},{1,3},{2,3}}
{{1},{3},{1,2},{2,3}}
{{2},{3},{1,2},{1,3}}
so a(30) = 3.
MATHEMATICA
bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
graprms[m_]:=Union[Table[Sort[Sort/@(m/.Rule@@@Table[{p[[i]], i}, {i, Length[p]}])], {p, Permutations[Union@@m]}]];
Table[Length[graprms[bpe/@bpe[n]]], {n, 0, 100}]
CROSSREFS
Positions of 1's are A330217.
Positions of first appearances are A330218.
The version for MM-numbers is A330098.
Achiral set-systems are counted by A083323.
BII-numbers of fully chiral set-systems are A330226.
Sequence in context: A228528 A366040 A219244 * A323017 A273638 A277582
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2019
STATUS
approved