TY - JOUR
T1 - Copy-paste trees and their growth rates
AU - Previte, Joseph
AU - Previte, Michelle
AU - Vanderschoot, Mary
PY - 2016/1/1
Y1 - 2016/1/1
N2 - 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 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 copypaste 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.
AB - 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 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 copypaste 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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U2 - 10.1216/RMJ-2016-46-3-1029
DO - 10.1216/RMJ-2016-46-3-1029
M3 - Article
AN - SCOPUS:84988916917
VL - 46
SP - 1029
EP - 1054
JO - Rocky Mountain Journal of Mathematics
JF - Rocky Mountain Journal of Mathematics
SN - 0035-7596
IS - 3
ER -