Mosaic Numbers of Fibonacci Trees

Heiko Harborth and Sabine Lohmann

A chapter in Applications of Fibonacci Numbers, 1990, pp 133-138 from Springer

Abstract: 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.

Keywords: General Bound; Adjacent Vertex; Mathematical Literature; Common Edge; Fibonacci Number (search for similar items in EconPapers)
Date: 1990
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DOI: 10.1007/978-94-009-1910-5_15

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