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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:

[1] 1. N. G. DE BRUIJN, Asymptotic methods in Analysis, North-Holland, Amsterdam, 1958. Zbl0082.04202 · Zbl 0082.04202
[2] 2. L. COMTET, Advanced Combinatorics, Reidel, Dordrecht-Holland, 1974. Zbl0283.05001 MR460128 · Zbl 0283.05001
[3] 3. H. PRODINGER, On the Number of Fibonacci Partitions of a Set, The Fibonacci Quarterly, Vol. 19, 1981, pp. 463-466. Zbl0475.05009 MR644710 · Zbl 0475.05009
[4] 4. J. RIORDAN, Combinatorial Identifies, Wiley, New York, 1968. Zbl0194.00502 MR231725 · Zbl 0194.00502
[5] 5. G.-C. ROTA, The Number of Partitions of a Set, American Math. Monthly, Vol.71, 1964, Zbl0121.01803 MR161805 · Zbl 0121.01803
[6] reprinted in G.-C. Rota : Finite Operator Calculus, Academic Press, New York, 1975. MR379213
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