

A327104


Maximum vertexdegree of the setsystem with BIInumber n.


7



0, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 2, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 2, 3, 1, 1, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 1, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 3, 3, 3, 2, 3, 2, 3, 3, 4, 3
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OFFSET

0,6


COMMENTS

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 setsystem with BIInumber n to be obtained by taking the binary indices of each binary index of n. Every setsystem (finite set of finite nonempty sets) has a different BIInumber. 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 BIInumber of {{2},{1,3}} is 18. Elements of a setsystem are sometimes called edges.
In a setsystem, the degree of a vertex is the number of edges containing it.


LINKS

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


EXAMPLE

The BIInumber of {{2},{3},{1,2},{1,3},{2,3}} is 62, and its degrees are (2,3,3), so a(62) = 3.


MATHEMATICA

bpe[n_]:=Join@@Position[Reverse[IntegerDigits[n, 2]], 1];
Table[If[n==0, 0, Max@@Length/@Split[Sort[Join@@bpe/@bpe[n]]]], {n, 0, 100}]


CROSSREFS

Positions of 1's are A326701 (BIInumbers of setpartitions).
The minimum vertexdegree is A327103.
Positions of 2's are A327106.
Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326786, A327041.
Sequence in context: A152906 A128522 A025454 * A126061 A088496 A036602
Adjacent sequences: A327101 A327102 A327103 * A327105 A327106 A327107


KEYWORD

nonn


AUTHOR

Gus Wiseman, Aug 26 2019


STATUS

approved



