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Uniform growth rate


Authors: Kasra Rafi and Jing Tao
Journal: Proc. Amer. Math. Soc. 144 (2016), 1415-1427
MSC (2010): Primary 20F36, 20F65, 57M07
DOI: https://doi.org/10.1090/proc/12816
Published electronically: December 22, 2015
MathSciNet review: 3451220
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Abstract: In an evolutionary system in which the rules of mutation are local in nature, the number of possible outcomes after $ m$ mutations is an exponential function of $ m$ but with a rate that depends only on the set of rules and not the size of the original object. We apply this principle to find a uniform upper bound for the growth rate of certain groups including the mapping class group. We also find a uniform upper bound for the growth rate of the number of homotopy classes of triangulations of an oriented surface that can be obtained from a given triangulation using $ m$ diagonal flips.


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Additional Information

Kasra Rafi
Affiliation: Department of Mathematics, University of Toronto, Toronto, Canada
Email: rafi@math.toronto.edu

Jing Tao
Affiliation: Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73019-0315
Email: jing@math.ou.edu

DOI: https://doi.org/10.1090/proc/12816
Received by editor(s): August 28, 2014
Received by editor(s) in revised form: April 9, 2015
Published electronically: December 22, 2015
Additional Notes: The first author was partially supported by NCERC Research Grant, RGPIN 435885.
The second author was partially supported by NSF Research Grant, DMS-1311834
Communicated by: Kevin Whyte
Article copyright: © Copyright 2015 American Mathematical Society

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