直角Coxeter群的散度和厚度特征

Pub Date : 2022-09-27 DOI:10.1112/topo.12267
Ivan Levcovitz
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引用次数: 4

摘要

我们完全分类了直角Coxeter群(racg)可能的散度函数。特别地,我们证明了任何这类群的散度要么是多项式的,要么是指数的,要么是无限的。证明了一个RACG是k阶强厚的当且仅当它的散度函数是k+1阶的多项式。此外,我们证明了RACG的确切散度函数可以很容易地从它的定义图中通过一个我们称为超图索引的不变量计算出来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Characterizing divergence and thickness in right-angled Coxeter groups

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Characterizing divergence and thickness in right-angled Coxeter groups

We completely classify the possible divergence functions for right-angled Coxeter groups (RACGs). In particular, we show that the divergence of any such group is either polynomial, exponential, or infinite. We prove that a RACG is strongly thick of order k $k$ if and only if its divergence function is a polynomial of degree k + 1 $k+1$ . Moreover, we show that the exact divergence function of a RACG can easily be computed from its defining graph by an invariant we call the hypergraph index.

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