Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bifix codes and Sturmian words   We prove new results concerning the relation between bifix codes, episturmian
words and subgroups offree groups. We study bifix codes in factorial sets of
words. We generalize most properties of ordinary maximal bifix codes to bifix
codes maximal in a recurrent set $F$ of words ($F$-maximal bifix codes). In the
case of bifix codes contained in Sturmian sets of words, we obtain several new
results. Let $F$ be a Sturmian set of words, defined as the set of factors of a
strict episturmian word. Our results express the fact that an $F$-maximal bifix
code of degree $d$ behaves just as the set of words of $F$ of length $d$. An
$F$-maximal bifix code of degree $d$ in a Sturmian set of words on an alphabet
with $k$ letters has $(k-1)d+1$ elements. This generalizes the fact that a
Sturmian set contains $(k-1)d+1$ words of length $d$. Moreover, given an
infinite word $x$, if there is a finite maximal bifix code $X$ of degree $d$
such that $x$ has at most $d$ factors of length $d$ in $X$, then $x$ is
ultimately periodic. Our main result states that any $F$-maximal bifix code of
degree $d$ on the alphabet $A$ is the basis of a subgroup of index $d$ of the
free group on~$A$.

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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: plasm-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
0
The categories of this paper are: hep-ph