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Lattice animals on a staircase and Fibonacci numbers

L. Turban
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Abstract

We study the statistics of column-convex lattice animals resulting from the stacking of squares on a single or double staircase. We obtain exact expressions for the number of animals with a given length and area, their mean length and their mean height. These objects are closely related to Fibonacci numbers. On a single staircase, the total number of animals with area k is given by the Fibonacci number F_k.

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L. Turban. 2000-11-02. Lattice animals on a staircase and Fibonacci numbers. https://doi.org/10.1088/0305-4470%2F33%2F13%2F311

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