Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Data about hyperbolic Coxeter systems   We collect several data about Coxeter systems (cf. [Bou07, Hum90]), with
particular emphasis on the hyperbolic ones. For each ($\preceq$-minimal)
hyperbolic Coxeter system (W,S) the Poincar\'e series \[p_{(W,S)}(t)=\sum_{w\in
W} t^{\ell(w)}\] and the growth rate \[ \omega(W,S)=\limsup_n \sqrt[n]{a_n}\]
are explicitly computed using Magma (cf. [BCP97]). These computations were
performed in connection to the proof of [Ter, Thm. B]. Since the Poincar\'e
series represents a rational function, one may recover the sequence
$(a_k)_{k\geq 0}$ through a linear recurrence relation on the coefficients,
provided that enough terms at the beginning of the sequence are known. For each
Coxeter system the initial coefficients $(a_k)_{k=0}^N$ are computed, where $N$
is the degree of the numerator of $p_{(W,S)}(t)$.

20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an