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\begin{document}

\begin{abstract}
Let $\FQ$ be the set of Farey fractions of order $Q$. 
Given the integers $\d\ge 2$ and $0\le \c \le \d-1$, let $\FQ(\c,\d)$ be
the subset of $\FQ$ of those fractions whose denominators are 
$\equiv \c$ (mod \  $\d )$, arranged in ascending order. The problem we
address here is to show that as $Q\to\infty$, 
there exists a limit probability measuring the distribution of $s$-tuples
of consecutive denominators of fractions in $\FQ(\c,\d)$.
This shows that the clusters of points
$(q_0/Q,q_1/Q,\dots,q_s/Q)\in[0,1]^{s+1}$, where $q_0,q_1,\dots,q_s$
are consecutive denominators of members of $\FQ$ produce a limit set,
denoted by $\D(\c,\d)$.
The shape and the structure of this set are presented in several
particular cases. 
\end{abstract}


\end{document}

                                                                                

