Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-20T06:25:51.279Z Has data issue: false hasContentIssue false
  • English
  • Français

Ordered Fibonacci Partitions

Published online by Cambridge University Press:  20 November 2018

Helmut Prodinger
Helmut Prodinger*
Affiliation:
Institut für Algebra und Diskrete Mathematik, Technische, Universitàt Wien, Gubhausstrabe 27-29, A-1040 Wien, Austria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Ordered partitions are enumerated by Fn = Σk k !S(n, k) where S(n, k) is the Stirling number of the second kind. We give some comments on several papers dealing with ordered partitions and turn then to ordered Fibonacci partitions of {1, ߪ, n}: If d is a fixed integer, the sets A appearing in the partition have to fulfill i, j ∈ A, i ≠ j ⟹ |i-j| ≥ d. The number of ordered Fibonacci partitions is determined.

Keywords

05A17
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 3 , 01 September 1983 , pp. 312 - 316
Copyright
Copyright © Canadian Mathematical Society 1983

References

1. Bartholemy, J. P., An asymptotic equivalent for the number of total preorders on a finite set, Discrete Mathematics 29 (1980), 311-313.Google Scholar
2. Comtet, L., Advanced Combinatorics, Reidel, D., Dordrecht (1974).Google Scholar
3. Gross, O. A., Preferential arrangements, American Math. Monthly, 69 (1962), 4-8.Google Scholar
4. Henrici, P., Applied and Computational Complex Analysis, Vol. 2, John Wiley, New York and Toronto (1974).Google Scholar
5. James, R. D., The factors of a squarefree integer, Canad. Math. Bull. 10 (1968), 733-735.Google Scholar
6. Rota, G.-C., The number of partitions of a set, American Math. Monthly, 71 (1964); reprinted in G.-C. Rota: Finite Operator Calculus, Academic Press, New York (1975).Google Scholar
7. Prodinger, H., On the number of Fibonacci partitions of a set, The Fibonacci Quarterly 19 (1981), 463-466.Google Scholar
8. Prodinger, H., Analysis of an algorithm to construct Fibonacci partitions, R.A.I.R.O., Theoretical Informatics, to appear.Google Scholar
9. Tanny, S. M., On some numbers related to the Bell numbers, Canad. Math. Bull. 17 (1975), 733-738.Google Scholar