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Mosaic Numbers of Fibonacci Trees

In: Applications of Fibonacci Numbers

Author

Listed:
  • Heiko Harborth
  • Sabine Lohmann

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.

Suggested Citation

  • Heiko Harborth & Sabine Lohmann, 1990. "Mosaic Numbers of Fibonacci Trees," Springer Books, in: G. E. Bergum & A. N. Philippou & A. F. Horadam (ed.), Applications of Fibonacci Numbers, pages 133-138, Springer.
    • Handle: RePEc:spr:sprchp:978-94-009-1910-5_15
    DOI: 10.1007/978-94-009-1910-5_15
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