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Mathematics > Number Theory

arXiv:1406.4293 (math)
[Submitted on 17 Jun 2014 (v1), last revised 20 May 2015 (this version, v3)]

Title:Labeled Fibonacci Trees

Authors:Stéphane Legendre
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Abstract:The study describes a class of integer labelings of the Fibonacci tree, the tree of descent introduced by Fibonacci. In these labelings, Fibonacci sequences appear along ascending branches of the tree, and it is shown that the labels at any level are consecutive integers. The set of labeled trees is a commutative group isomorphic to $\mathbb{Z}^2$, and is endowed with an order relation. Properties of the Wythoff array are recovered as a special instance, and further properties of the labeled Fibonacci trees are described. These trees can be viewed as generalizations of the Wythoff array.
Comments: 17 pages, 6 figures
Subjects: Number Theory (math.NT); Combinatorics (math.CO)
Cite as: arXiv:1406.4293 [math.NT]
  (or arXiv:1406.4293v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1406.4293
Journal reference: Legendre S. 2015. Labeled Fibonacci trees. The Fibonacci Quarterly 53: 152-167

Submission history

From: Stephane Legendre [view email]
[v1] Tue, 17 Jun 2014 09:45:59 UTC (17 KB)
[v2] Tue, 8 Jul 2014 10:13:37 UTC (86 KB)
[v3] Wed, 20 May 2015 11:52:11 UTC (17 KB)
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