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\noindent
 {\bf  Toufik Mansour and Alek Vainshtein}
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\noindent {\bf Restricted permutations, continued fractions, and }

\noindent{\bf Chebyshev polynomials}
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Let $f_n^r(k)$ be the number of 132-avoiding permutations on
$n$ letters that contain exactly $r$ occurrences of $12\dots k$,
and let $F_r(x;k)$ and $F(x,y;k)$ be the generating functions defined by
$F_r(x;k)=\sum_{n\ge 0} f_n^r(k)x^n$ and $F(x,y;k)=\sum_{r\ge 0}F_r(x;k)y^r$.
We find an explicit expression for $F(x,y;k)$ in the form of a continued
fraction. This allows us to express $F_r(x;k)$ for $1\le r\le k$ via Chebyshev
polynomials of the second kind.

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