Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The finite index basis property   We describe in this paper a connection between bifix codes, symbolic
dynamical systems and free groups. This is in the spirit of the connection
established previously for the symbolic systems corresponding to Sturmian
words. We introduce a class of sets of factors of an infinite word with linear
factor complexity containing Sturmian sets and regular interval exchange sets,
namemly the class of tree sets. We prove as a main result that for a uniformly
recurrent tree set $F$, a finite bifix code $X$ on the alphabet $A$ is
$F$-maximal of $F$-degree $d$ if and only if it is the basis of a subgroup of
index $d$ of the free group on $A$.

35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex