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A327104 Maximum vertex-degree of the set-system with BII-number 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 (list; graph; refs; listen; history; text; internal format)
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 set-system with BII-number n to be obtained by taking the binary indices of each binary index of n. Every set-system (finite set of finite nonempty sets) 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.

In a set-system, the degree of a vertex is the number of edges containing it.

LINKS

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

EXAMPLE

The BII-number 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 (BII-numbers of set-partitions).

The minimum vertex-degree 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

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Last modified September 23 14:40 EDT 2021. Contains 347618 sequences. (Running on oeis4.)