A327103 Minimum vertex-degree in the set-system with BII-number n.

0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 2, 2, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2

Offset

0,8

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..87.

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) = 2.

Mathematica

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

Crossrefs

The maximum vertex-degree is A327104.

Positions of 1's are A327105.

Positions of terms > 1 are A327107.

Cf. A000120, A048793, A058891, A070939, A326031, A326701, A326783, A326786, A327041, A327228, A327229.

Sequence in context: A113515 A103754 A058665 * A290105 A191898 A043290

Adjacent sequences: A327100 A327101 A327102 * A327104 A327105 A327106

Keyword

nonn

Author

Gus Wiseman, Aug 26 2019

Status

approved