\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{insertion}
{\sc Albert, M.~H., Linton, S., and Ru\v{s}kuc, N.}
\newblock The insertion encoding of permutations.
\newblock {\em Electron. J. Combin. 12}, 1 (2005), Research paper 47, 31 pp.
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\bibitem{a:skewmerged}
{\sc Atkinson, M.~D.}
\newblock Permutations which are the union of an increasing and a decreasing
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\newblock {\em Electron. J. Combin. 5\/} (1998), Research paper 6, 13 pp.\
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\bibitem{atkinson:permuting-mecha:}
{\sc Atkinson, M.~D., and Beals, R.}
\newblock Permuting mechanisms and closed classes of permutations.
\newblock In {\em Combinatorics, Computation \& Logic '99 (Auckland)}, vol.~21
  of {\em Aust. Comput. Sci. Commun.} Springer, Singapore, 1999, pp.~117--127.

\bibitem{atkinson:partially-well-:}
{\sc Atkinson, M.~D., Murphy, M.~M., and Ru{\v{s}}kuc, N.}
\newblock Partially well-ordered closed sets of permutations.
\newblock {\em Order 19}, 2 (2002), 101--113.

\bibitem{atkinson:sorting-with-tw:}
{\sc Atkinson, M.~D., Murphy, M.~M., and Ru{\v{s}}kuc, N.}
\newblock Sorting with two ordered stacks in series.
\newblock {\em Theoret. Comput. Sci. 289}, 1 (2002), 205--223.

\bibitem{amr:natural}
{\sc Atkinson, M.~D., Murphy, M.~M., and Ru{\v{s}}kuc, N.}
\newblock Pattern avoidance classes and subpermutations.
\newblock {\em Electron. J. Combin. 12}, 1 (2005), Research paper 60, 18 pp.
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\bibitem{eco:survey}
{\sc Barcucci, E., Del~Lungo, A., Pergola, E., and Pinzani, R.}
\newblock E{CO}: a methodology for the enumeration of combinatorial objects.
\newblock {\em J. Differ. Equations Appl. 5}, 4-5 (1999), 435--490.

\bibitem{billey:kazhdan-lusztig:}
{\sc Billey, S.~C., and Warrington, G.~S.}
\newblock Kazhdan-{L}usztig polynomials for 321-hexagon-avoiding permutations.
\newblock {\em J. Algebraic Combin. 13}, 2 (2001), 111--136.

\bibitem{bose:matching}
{\sc Bose, P., Buss, J.~F., and Lubiw, A.}
\newblock Pattern matching for permutations.
\newblock {\em Inform. Process. Lett. 65}, 5 (1998), 277--283.

\bibitem{bm:four}
{\sc Bousquet-M{\'e}lou, M.}
\newblock Four classes of pattern-avoiding permutations under one roof:
  generating trees with two labels.
\newblock {\em Electron. J. Combin. 9}, 2 (2003), Research paper 19, 31 pp.
  (electronic).

\bibitem{brignall:simple-permutat:b}
{\sc Brignall, R., Ru\v{s}kuc, N., and Vatter, V.}
\newblock Simple permutations: decidability and unavoidable substructures.
\newblock arXiv:math.CO/0609211.

\bibitem{bdpr:eps}
{\sc Brlek, S., Duchi, E., Pergola, E., and Rinaldi, S.}
\newblock On the equivalence problem for succession rules.
\newblock {\em Discrete Math. 298}, 1-3 (2005), 142--154.

\bibitem{chow:forbidden-subse:}
{\sc Chow, T., and West, J.}
\newblock Forbidden subsequences and {C}hebyshev polynomials.
\newblock {\em Discrete Math. 204}, 1-3 (1999), 119--128.

\bibitem{chung:the-number-of-b:}
{\sc Chung, F. R.~K., Graham, R.~L., Hoggatt, Jr., V.~E., and Kleiman, M.}
\newblock The number of {B}axter permutations.
\newblock {\em J. Combin. Theory Ser. A 24}, 3 (1978), 382--394.

\bibitem{corneil:complement-redu:}
{\sc Corneil, D.~G., Lerchs, H., and Burlingham, L.~S.}
\newblock Complement reducible graphs.
\newblock {\em Discrete Appl. Math. 3}, 3 (1981), 163--174.

\bibitem{elder:problems-and-co:}
{\sc Elder, M., and Vatter, V.}
\newblock Problems and conjectures presented at the {T}hird {I}nternational
  {C}onference on {P}ermutation {P}atterns, {U}niversity of {F}lorida, {M}arch
  7--11, 2005.
\newblock arXiv:math.CO/0505504.

\bibitem{es:acpig}
{\sc Erd{\H{o}}s, P., and Szekeres, G.}
\newblock A combinatorial problem in geometry.
\newblock {\em Compos. Math. 2\/} (1935), 463--470.

\bibitem{gessel:symmetric-funct:}
{\sc Gessel, I.~M.}
\newblock Symmetric functions and {$P$}-recursiveness.
\newblock {\em J. Combin. Theory Ser. A 53}, 2 (1990), 257--285.

\bibitem{gl:fb}
{\sc Green, R.~M., and Losonczy, J.}
\newblock Freely braided elements of {C}oxeter groups.
\newblock {\em Ann. Comb. 6}, 3-4 (2002), 337--348.

\bibitem{knuth:the-art-of-comp:}
{\sc Knuth, D.~E.}
\newblock {\em The art of computer programming. {V}ol. 1: {F}undamental
  algorithms}.
\newblock Addison-Wesley Publishing Co., Reading, Mass., 1969.

\bibitem{k:sn}
{\sc Kremer, D.}
\newblock Permutations with forbidden subsequences and a generalized
  {S}chr\"oder number.
\newblock {\em Discrete Math. 218}, 1-3 (2000), 121--130.

\bibitem{ks:len4}
{\sc Kremer, D., and Shiu, W.~C.}
\newblock Finite transition matrices for permutations avoiding pairs of length
  four patterns.
\newblock {\em Discrete Math. 268}, 1-3 (2003), 171--183.

\bibitem{le:wilf-classes-of:}
{\sc Le, I.}
\newblock Wilf classes of pairs of permutations of length 4.
\newblock {\em Electron. J. Combin. 12\/} (2005), Research Paper 25, 27 pp.
  (electronic).

\bibitem{macmahon:combinatory-ana:}
{\sc MacMahon, P.~A.}
\newblock {\em Combinatory Analysis}.
\newblock Cambridge University Press, London, 1915/16.

\bibitem{mansour:permutations-co:}
{\sc Mansour, T.}
\newblock Permutations containing and avoiding certain patterns.
\newblock In {\em Formal power series and algebraic combinatorics (Moscow,
  2000)}. Springer, Berlin, 2000, pp.~704--708.

\bibitem{mansour:fb}
{\sc Mansour, T.}
\newblock On an open problem of {G}reen and {L}osonczy: exact enumeration of
  freely braided permutations.
\newblock {\em Discrete Math. Theor. Comput. Sci. 6}, 2 (2004), 461--470.

\bibitem{mansour:321-polygon-avo:}
{\sc Mansour, T., and Stankova, Z.}
\newblock $321$-polygon-avoiding permutations and {C}hebyshev polynomials.
\newblock {\em Electron. J. Combin. 9}, 2 (2003), Research paper 5, 16 pp.
  (electronic).

\bibitem{mohring:substitution-de:}
{\sc M{\"o}hring, R.~H., and Radermacher, F.~J.}
\newblock Substitution decomposition for discrete structures and connections
  with combinatorial optimization.
\newblock In {\em Algebraic and combinatorial methods in operations research},
  vol.~95 of {\em North-Holland Math. Stud.} North-Holland, Amsterdam, 1984,
  pp.~257--355.

\bibitem{nw:wqo}
{\sc Nash-Williams, C. S. J.~A.}
\newblock On well-quasi-ordering finite trees.
\newblock {\em Proc. Cambridge Philos. Soc. 59\/} (1963), 833--835.

\bibitem{sloane:the-on-line-enc:}
{\sc Sloane, N. J.~A.}
\newblock The {O}n-line {E}ncyclopedia of {I}nteger {S}equences.
\newblock Available online at
  {http://www.research.att.com/\~{}njas/sequences/}.

\bibitem{stankova:explicit-enumer:}
{\sc Stankova, Z., and West, J.}
\newblock Explicit enumeration of $321$, hexagon-avoiding permutations.
\newblock {\em Discrete Math. 280}, 1-3 (2004), 165--189.

\bibitem{stankova:fs}
{\sc Stankova, Z.~E.}
\newblock Forbidden subsequences.
\newblock {\em Discrete Math. 132}, 1-3 (1994), 291--316.

\bibitem{stanley:enumerative-com:}
{\sc Stanley, R.~P.}
\newblock {\em Enumerative combinatorics. {V}ol. 1}, vol.~49 of {\em Cambridge
  Studies in Advanced Mathematics}.
\newblock Cambridge University Press, Cambridge, 1997.

\bibitem{stanley:enumerative-com:a}
{\sc Stanley, R.~P.}
\newblock {\em Enumerative combinatorics. {V}ol. 2}, vol.~62 of {\em Cambridge
  Studies in Advanced Mathematics}.
\newblock Cambridge University Press, Cambridge, 1999.

\bibitem{vatter:finitely-labele:}
{\sc Vatter, V.}
\newblock Finitely labeled generating trees and restricted permutations.
\newblock {\em J. Symbolic Comput. 41}, 5 (2006), 559--572.

\bibitem{west:generating-tree:a}
{\sc West, J.}
\newblock Generating trees and the {C}atalan and {S}chr\"oder numbers.
\newblock {\em Discrete Math. 146}, 1-3 (1995), 247--262.

\bibitem{west:generating-tree:}
{\sc West, J.}
\newblock Generating trees and forbidden subsequences.
\newblock {\em Discrete Math. 157}, 1-3 (1996), 363--374.

\bibitem{wilf:what-is-an-answ:}
{\sc Wilf, H.~S.}
\newblock What is an answer?
\newblock {\em Amer. Math. Monthly 89}, 5 (1982), 289--292.

\bibitem{zeilberger:enumeration-sch:}
{\sc Zeilberger, D.}
\newblock Enumeration schemes and, more importantly, their automatic
  generation.
\newblock {\em Ann. Comb. 2}, 2 (1998), 185--195.

\end{thebibliography}