\begin{thebibliography}{10}

\bibitem{partition}
G.E. Andrews, {\em The theory of partitions}, Addison-Wesley Publishing Co.,
  Reading, Mass.-London-Amsterdam, 1976.
\newblock Encyclopedia of Mathematics and its Applications, Vol. 2.

\bibitem{qbinomial}
J.~Azose, A tiling interpretation of $q$-binomial coefficients.
\newblock Thesis, Harvey Mudd College, 2007.

\bibitem{vincular}
Eric Babson and Einar Steingr{\'{\i}}msson, Generalized permutation patterns
  and a classification of the {M}ahonian statistics, {\em S\'em. Lothar.
  Combin.} {\bf 44} (2000), Art. B44b, 18 pp. (electronic).

\bibitem{bivincular}
M.~Bousquet-M{\'e}lou, A.~Claesson, M.~Dukes, and S.~Kitaev, {$(2+2)$}-free
  posets, ascent sequences and pattern avoiding permutations, {\em J. Combin.
  Theory Ser. A} {\bf 117}(7) (2010), 884--909.

\bibitem{mesh}
P.~Br{\"a}nd{\'e}n and A.~Claesson, Mesh patterns and the expansion of
  permutation statistics as sums of permutation patterns, {\em Electron. J.
  Combin.} {\bf 18}(2) (2011), Paper 5, 14.

\bibitem{bijection}
A.~Claesson and S.~Kitaev, Classification of bijections between 321- and
  132-avoiding permutations.
\newblock In {\em 20th {A}nnual {I}nternational {C}onference on {F}ormal
  {P}ower {S}eries and {A}lgebraic {C}ombinatorics ({FPSAC} 2008)}, Discrete
  Math. Theor. Comput. Sci. Proc., AJ, pp.  495--506. Assoc. Discrete Math.
  Theor. Comput. Sci., Nancy, 2008.

\bibitem{vincularpair}
A.~Claesson and T.~Mansour, Enumerating permutations avoiding a pair of
  {B}abson-{S}teingr\'\i msson patterns, {\em Ars Combin.} {\bf 77} (2005),
  17--31.

\bibitem{actualmotzkin}
Robert Donaghey and Louis~W. Shapiro, Motzkin numbers, {\em J. Combinatorial
  Theory Ser. A} {\bf 23}(3) (1977), 291--301.

\bibitem{motzkinbijection}
Sergi Elizalde and Toufik Mansour, Restricted {M}otzkin permutations, {M}otzkin
  paths, continued fractions and {C}hebyshev polynomials, {\em Discrete Math.}
  {\bf 305}(1-3) (2005), 170--189.

\bibitem{ElizaldeNoy}
Sergi Elizalde and Marc Noy, {Consecutive patterns in permutations}, {\em
  Advances in Applied Mathematics} {\bf 30}(1-2) (2003), 110--125.

\bibitem{hammersley}
J.~M. Hammersley, A few seedlings of research, In {\em Proceedings of the
  {S}ixth {B}erkeley {S}ymposium on {M}athematical {S}tatistics and
  {P}robability ({U}niv. {C}alifornia, {B}erkeley, {C}alif., 1970/1971), {V}ol.
  {I}: {T}heory of statistics}, pp.  345--394. Univ. California Press,
  Berkeley, Calif., 1972.

\bibitem{shading}
I.~Hilmarsson, I.~J\'{o}nsd\'{o}ttir, S.~Sigur{\dh}ard\'{o}ttir,
  L.~Vi{\dh}arsd\'{o}ttir, and H.~Ulfarsson, Wilf-classification of mesh
  patterns of short length.
\newblock arXiv:1409.3165v3, 2014.

\bibitem{multiconsecutive}
Sergey Kitaev, Multi-avoidance of generalised patterns, {\em Discrete Math.}
  {\bf 260}(1-3) (2003), 89--100.

\bibitem{classical}
D.E. Knuth, {\em The art of computer programming. {V}ol. 3}, Addison-Wesley,
  Reading, MA, 1998.
\newblock Sorting and searching, Second edition.

\bibitem{barpatt}
L.~Pudwell, Enumeration schemes for permutations avoiding barred patterns, {\em
  Electron. J. Combin.} {\bf 17}(1) (2010), Research Paper 29, 27.

\bibitem{rogers}
D.G. Rogers, Ascending sequences in permutations, {\em Discrete Math.} {\bf
  22}(1) (1978), 35--40.

\bibitem{classicsubset}
R.~Simion and F.W. Schmidt, Restricted permutations, {\em European J. Combin.}
  {\bf 6}(4) (1985), 383--406.

\bibitem{motzkin}
N.~Sloane, The on-line encyclopedia of integer sequences.
\newblock published electronically at http://oeis.org, 2010.

\bibitem{west3}
H.~Ulfarsson, Describing {W}est-3-stack-sortable permutations with permutation
  patterns, {\em S\'em. Lothar. Combin.} {\bf 67} (2011/12), Art. B67d, 20.

\bibitem{westbar}
Julian West, Sorting twice through a stack, {\em Theoret. Comput. Sci.} {\bf
  117}(1-2) (1993), 303--313.
\newblock Conference on Formal Power Series and Algebraic Combinatorics
  (Bordeaux, 1991).

\end{thebibliography}
