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.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 09 2019
STATUS
approved