The Fibonacci Shuffle Tree

Peter G. Anderson

A chapter in Applications of Fibonacci Numbers, 1998, pp 9-16 from Springer

Abstract: Abstract We introduce the Fibonacci Shuffle Tree (FST) which is an infinite binary tree with nodes 0, 1, 2,…. The FST is a binary search tree if we associate the key {kα} with node k for each k = 0, 1, 2, …, where α = (1 + √5/2 and {x} denotes the fractional part of x. If F[ k] denotes a subtree of the FST induced by nodes 0, 1, 2, …, k, then F[k] can be obtained from F[k - 1] by standard binary tree insertion of the key {k α} into F[ k - 1].

Keywords: Binary Tree; Regular Expression; Binary Search Tree; Left Child; Partial Quotient (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-94-011-5020-0_2

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