Abstract
Different meanings of Fibonacci trees are used in the mathematical literature. Here we will consider those drawings of trees which represent the old rabbit story as in V. E. Hoggatt’s book [3], p. 2. These Fibonacci trees T n will be realized as polyominoes in the square grid such that vertices correspond to unit squares and edges to certain strings of edge-to-edge unit squares. Because of their patterns we will call these realizations mosaics of T n . Subsequently we define the mosaic number M( n ) of T n to be the smallest number of unit squares which are necessary for realizations of T n . It is the purpose of this note to determine general bounds of M(n) and exact values for small n.
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References
Alfred, Brother U. “Dying Rabbit Problem Revived.” The Fibonacci Quarterly, Vol. 1, No. 4 (1963): pp. 53–56.
Golomb, S. W. Polyominoes. Charles Sribner’s, New York (1965).
Hoggatt, Jr., V. E. Fibonacci and Lucas Numbers. Houghton Mifflin Co., Boston (1969).
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© 1990 Kluwer Academic Publishers
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Harborth, H., Lohmann, S. (1990). Mosaic Numbers of Fibonacci Trees. In: Bergum, G.E., Philippou, A.N., Horadam, A.F. (eds) Applications of Fibonacci Numbers. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1910-5_15
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DOI: https://doi.org/10.1007/978-94-009-1910-5_15
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7352-3
Online ISBN: 978-94-009-1910-5
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