膨胀复合体的生长级数
Growth series for expansion complexes
摘要：
本文研究有限细分规则下扩张复形的增长级数。设X是一个有限剖分规则的展开复形，它具有有界的价，网格接近于0，S是X的一个种子。我们可以通过在种子范数0中给出图块，然后使用瘦路径范数或胖路径范数来递归地定义其他图块的范数，来定义（X，S）的增长序列。主要定理是，关于这两个范数中的任何一个，（X，S）的增长级数具有多项式增长。此外，双曲展开复形的增长率在射线中的阶数是稠密的[2，\infty）.
英文摘要：
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).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
