\def\cprime{$'$}
\begin{thebibliography}{10}

\bibitem{albert:simple-permutat:}
{\sc Albert, M.~H., and Atkinson, M.~D.}
\newblock Simple permutations and pattern restricted permutations.
\newblock {\em Discrete Math. 300}, 1-3 (2005), 1--15.

\bibitem{albert:the-enumeration:}
{\sc Albert, M.~H., Atkinson, M.~D., and Klazar, M.}
\newblock The enumeration of simple permutations.
\newblock {\em J. Integer Seq. 6}, 4 (2003), Article 03.4.4, 18 pp.
  (electronic).

\bibitem{atkinson:restricted-perm:}
{\sc Atkinson, M.~D.}
\newblock Restricted permutations.
\newblock {\em Discrete Math. 195}, 1-3 (1999), 27--38.

\bibitem{babson:generalized-per:}
{\sc Babson, E., and Steingr{\'{\i}}msson, E.}
\newblock Generalized permutation patterns and a classification of the
  {M}ahonian statistics.
\newblock {\em S\'em. Lothar. Combin. 44\/} (2000), Art. B44b, 18 pp.
  (electronic).

\bibitem{bona:the-number-of-p:}
{\sc B{\'o}na, M.}
\newblock The number of permutations with exactly {$r$} {$132$}-subsequences is
  {$P$}-recursive in the size!
\newblock {\em Adv. in Appl. Math. 18}, 4 (1997), 510--522.

\bibitem{bona:permutations-wi:}
{\sc B{\'o}na, M.}
\newblock Permutations with one or two {$132$}-subsequences.
\newblock {\em Discrete Math. 181}, 1-3 (1998), 267--274.

\bibitem{brignall:simple-permutat:}
{\sc Brignall, R., Huczynska, S., and Vatter, V.}
\newblock Simple permutations and algebraic generating functions.
\newblock \texttt{arXiv:math.CO/0606186}.

\bibitem{brignall:simple-permutat:b}
{\sc Brignall, R., Ru\v{s}kuc, N., and Vatter, V.}
\newblock Simple permutations: decidability and unavoidable substructures.
\newblock In preparation.

\bibitem{claesson:counting-occurr:}
{\sc Claesson, A., and Mansour, T.}
\newblock Counting occurrences of a pattern of type $(1,2)$ or $(2,1)$ in
  permutations.
\newblock {\em Adv. in Appl. Math. 29}, 2 (2002), 293--310.

\bibitem{corteel:common-interval:}
{\sc Corteel, S., Louchard, G., and Pemantle, R.}
\newblock Common intervals of permutations.
\newblock In {\em Mathematics and computer science. III}, Trends Math.
  Birkh\"auser, Basel, 2004, pp.~3--14.

\bibitem{ehrenfeucht:the-theory-of-2:}
{\sc Ehrenfeucht, A., Harju, T., and Rozenberg, G.}
\newblock {\em The theory of {$2$}-structures}.
\newblock World Scientific Publishing Co. Inc., River Edge, NJ, 1999.

\bibitem{foldes:on-intervals-in:}
{\sc F{\"o}ldes, S.}
\newblock On intervals in relational structures.
\newblock {\em Z. Math. Logik Grundlag. Math. 26}, 2 (1980), 97--101.

\bibitem{fulmek:enumeration-of-:}
{\sc Fulmek, M.}
\newblock Enumeration of permutations containing a prescribed number of
  occurrences of a pattern of length three.
\newblock {\em Adv. in Appl. Math. 30}, 4 (2003), 607--632.

\bibitem{ille:indecomposable-:}
{\sc Ille, P.}
\newblock Indecomposable graphs.
\newblock {\em Discrete Math. 173}, 1-3 (1997), 71--78.

\bibitem{mansour:restricted-132-:}
{\sc Mansour, T.}
\newblock Restricted $132$-alternating permutations and {C}hebyshev
  polynomials.
\newblock {\em Ann. Comb. 7}, 2 (2003), 201--227.

\bibitem{mansour:counting-occurr:a}
{\sc Mansour, T.}
\newblock Counting occurrences of $132$ in an even permutation.
\newblock {\em Int. J. Math. Math. Sci.}, 25-28 (2004), 1329--1341.

\bibitem{mansour:counting-occurr:}
{\sc Mansour, T., and Vainshtein, A.}
\newblock Counting occurrences of $132$ in a permutation.
\newblock {\em Adv. in Appl. Math. 28}, 2 (2002), 185--195.

\bibitem{mansour:counting-occurr:b}
{\sc Mansour, T., Yan, S. H.~F., and Yang, L. L.~M.}
\newblock Counting occurrences of $231$ in an involution.
\newblock {\em Discrete Math. 306}, 6 (2006), 564--572.

\bibitem{noonan:the-number-of-p:}
{\sc Noonan, J.}
\newblock The number of permutations containing exactly one increasing
  subsequence of length three.
\newblock {\em Discrete Math. 152}, 1-3 (1996), 307--313.

\bibitem{noonan:the-enumeration:}
{\sc Noonan, J., and Zeilberger, D.}
\newblock The enumeration of permutations with a prescribed number of
  ``forbidden'' patterns.
\newblock {\em Adv. in Appl. Math. 17}, 4 (1996), 381--407.

\bibitem{sabidussi:graph-derivativ:}
{\sc Sabidussi, G.}
\newblock Graph derivatives.
\newblock {\em Math. Z. 76\/} (1961), 385--401.

\end{thebibliography}