Open Access
2016 Copy-paste trees and their growth rates
Joseph Previte, Michelle Previte, Mary Vanderschoot
Rocky Mountain J. Math. 46(3): 1029-1054 (2016). DOI: 10.1216/RMJ-2016-46-3-1029


In this paper, we describe a copy-and-paste method for constructing a class of infinite self-similar trees. A copy-paste tree is constructed by repeatedly attaching copies of a finite tree (called a \textit {generator}) to certain designated attachment vertices. We show that each generator has an associated nonnegative matrix which can be used to determine a formula for the growth function of the copy-paste tree. In our main theorem, we use results from Perron-Frobenius theory to show that every copy-paste tree has exponential growth, with growth rate equal to the spectral radius of its associated matrix.


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Joseph Previte. Michelle Previte. Mary Vanderschoot. "Copy-paste trees and their growth rates." Rocky Mountain J. Math. 46 (3) 1029 - 1054, 2016.


Published: 2016
First available in Project Euclid: 7 September 2016

zbMATH: 1345.05014
MathSciNet: MR3544844
Digital Object Identifier: 10.1216/RMJ-2016-46-3-1029

Primary: 05C05 , 05C10 , 05C50

Keywords: exponential growth , Perron-Frobenius theory , trees , vertex replacement rules

Rights: Copyright © 2016 Rocky Mountain Mathematics Consortium

Vol.46 • No. 3 • 2016
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