## Analysis of an algorithm to construct Fibonacci partitions.(English)Zbl 0562.05006

A Fibonacci partition of $$\{$$ 1,2,...,n$$\}$$ is a partition such that i and $$i+1$$ are never in the same block, the corresponding number $$C_ n$$ equals $$B_ n$$ in the number of partitions of $$\{$$ 1,2,...,n-1$$\}$$. There exists an algorithm which constructs a unique Fibonacci partition of $$\{1,2,..,n+1\}$$ from a partition of $$\{$$ 1,2,...,n$$\}$$. Let $$C_{n+1,k}$$ be the number of companions of $$(n+1)$$ in the Fibonacci partitions. Exact formulas and asymptotic estimates for the average and the variance of these numbers are given.
Reviewer: M.Cheema

### MSC:

 05A17 Combinatorial aspects of partitions of integers 05A15 Exact enumeration problems, generating functions 11P81 Elementary theory of partitions
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### References:

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