Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorial Properties of primitive words with Non-primitive Product   Let $\mathcal{A}$ be an alphabet of size $n\ge 2$. In this paper, we give a
complete description of primitive words $p\neq q$ over an alphabet
$\mathcal{A}$ of size $n\geq2$ such that $pq$ is non-primitive and $|p|=2|q|$.
In particular, if $l$ is s a positive integer, we count the cardinality of the
set $\mathcal{E}(l,\mathcal{A})$ of all couples $(p,q)$ of primitive words such
that $|p|=2|q|=2l$ and $pq$ is non-primitive. Then we give a combinatorial
formula for this cardinality and its asymptotic behavior, as $l$ or $n$ goes to
infinity.

14
The categories of this paper are: math-ph
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th