Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Freeness of Sch\"utzenberger groups of primitive substitutions   Our main goal is to study the freeness of Sch\"utzenberger groups defined by
primitive substitutions. Our findings include a simple freeness test for these
groups, which is applied to exhibit a primitive invertible substitution with
corresponding non-free Sch\"utzenberger group. This constitutes a
counterexample to a result of Almeida dating back to 2005. We also give some
early results concerning relative freeness of Sch\"utzenberger groups, a
question which remains largely unexplored.

11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc