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A327104
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Maximum vertex-degree of the set-system with BII-number n.
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7
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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
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0,6
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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Positions of 1's are A326701 (BII-numbers of set-partitions).
The minimum vertex-degree is A327103.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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