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


05A17 Combinatorial aspects of partitions of integers
05A15 Exact enumeration problems, generating functions
11P81 Elementary theory of partitions
Full Text: EuDML


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