dc.contributor.author Cannon, JW en_US dc.contributor.author Floyd, WJ en_US dc.contributor.author Parry, WR en_US dc.date.accessioned 2017-01-14T01:45:24Z dc.date.available 2017-01-14T01:45:24Z dc.identifier.uri http://hdl.handle.net/10919/74306 dc.description.abstract This paper is concerned with growth series for expansion complexes for finite subdivision rules. Suppose X is an expansion complex for a finite subdivision rule with bounded valence and mesh approaching 0, and let S be a seed for X. One can define a growth series for (X,S) by giving the tiles in the seed norm 0 and then using either the skinny path norm or the fat path norm to recursively define norms for the other tiles. The main theorem is that, with respect to either of these norms, the growth series for (X,S) has polynomial growth. Furthermore, the degrees of the growth rates of hyperbolic expansion complexes are dense in the ray [2,\infty). en_US dc.relation.uri http://arxiv.org/abs/1612.04771v1 en_US dc.subject math.DS en_US dc.subject math.DS en_US dc.subject 52C20, 52C26 (Primary), 05B45, 30F45 (Secondary) en_US dc.title Growth series for expansion complexes en_US dc.type Article - Refereed dc.description.notes 11 pages, 6 figures en_US pubs.organisational-group /Virginia Tech pubs.organisational-group /Virginia Tech/All T&R Faculty pubs.organisational-group /Virginia Tech/Science pubs.organisational-group /Virginia Tech/Science/COS T&R Faculty pubs.organisational-group /Virginia Tech/Science/Mathematics
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