Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the rank of a Coxeter group   Let W be a Coxeter group with Coxeter generators S. The rank of the Coxeter
system (W,S) is the cardinality |S| of S. The Coxeter system (W,S) has finite
rank if and only if W is finitely generated. If (W,S) has infinite rank, then
|S| = |W|, since every element of W is represented by a finite product of
elements of S. Thus if W is not finitely generated, the rank of (W,S) is
uniquely determined by W. If W is finitely generated, then W may have sets of
Coxeter generators S and S' of different ranks. In this paper, we determine the
set of all possible ranks for an arbitrary finitely generated Coxeter group W.

34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat