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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=0..86.

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.

Cf. A000120, A003238, A007716, A016031, A048793, A055621, A070939, A214577, A326031, A326702, A330101, A330195, A330229, A330230, A330233.

Sequence in context: A227736 A228528 A219244 * A323017 A273638 A277582

Adjacent sequences:  A330228 A330229 A330230 * A330232 A330233 A330234

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 09 2019

STATUS

approved

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Last modified September 29 16:23 EDT 2022. Contains 357090 sequences. (Running on oeis4.)