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\providecommand{\natexlab}[1]{#1}

\bibitem[{Aho and Ullman(1972)}]{AhoUll72}
Albert~V. Aho and Jeffery~D. Ullman.
\newblock \emph{The Theory of Parsing, Translation, and Compiling}, volume~1.
\newblock Prentice-Hall, Englewood Cliffs, NJ, 1972.

\bibitem[{Albert et~al.(2003)Albert, Atkinson, and
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M.~H. Albert, M.~D. Atkinson, and M.~Klazar.
\newblock The enumeration of simple permutations.
\newblock \emph{Journal of Integer Sequences} \textbf{6} (2003), 18 pages.

\bibitem[{Bui-Xuan et~al.(2005)Bui-Xuan, Habib, and Paul}]{BuiXuan05}
Binh~Minh Bui-Xuan, Michel Habib, and Christophe Paul.
\newblock Revisiting {T. Uno} and {M. Yagiura}'s algorithm.
\newblock In \emph{The 16th Annual International Symposium on Algorithms and
  Computation (ISAAC'05)}. 2005, pp. 146--155.

\bibitem[{Flajolet and Sedgewick(2001)}]{FlSe01}
Philippe Flajolet and Robert Sedgewick.
\newblock Analytic combinatorics: Functional equations, rational and algebraic
  functions.
\newblock Technical Report 4103, INRIA, 2001.
\newblock 98 pages.

\bibitem[{Heber and Stoye(2001)}]{HeberStoye01}
Steffen Heber and Jens Stoye.
\newblock Finding all common intervals of k permutations.
\newblock In \emph{Combinatorial Pattern Matching, 12th Annual Symposium}.
  Springer-Verlag, 2001, pp. 207--218.

\bibitem[{Landau et~al.(2005)Landau, Parida, and Weimann}]{Landau05}
Gad~M. Landau, Laxmi Parida, and Oren Weimann.
\newblock Gene proximity analysis across whole genomes via {PQ} trees.
\newblock \emph{Journal of Computational Biology} \textbf{12} (2005),
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\bibitem[{Melamed(2003)}]{Melamed-naacl03}
I.~Dan Melamed.
\newblock Multitext grammars and synchronous parsers.
\newblock In \emph{Proceedings of the 2003 Meeting of the North American
  chapter of the Association for Computational Linguistics (NAACL-03)}.
  Edmonton, 2003.

\bibitem[{Odlyzko(1995)}]{Odlyzko95}
Andrew Odlyzko.
\newblock Asymptotic enumeration methods.
\newblock In R.~L. Graham, M.~Groetschel, and L.~Lovasz, editors,
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\bibitem[{Satta and Peserico(2005)}]{SattaPeserico05}
Giorgio Satta and Enoch Peserico.
\newblock Some computational complexity results for synchronous context-free
  grammars.
\newblock In \emph{Proceedings of Human Language Technology Conference and
  Conference on Empirical Methods in Natural Language Processing (HLT/EMNLP)}.
  Vancouver, Canada, 2005, pp. 803--810.

\bibitem[{Shapiro and Stephens(1991)}]{ShapiroStephens91}
L.~Shapiro and A.~B. Stephens.
\newblock Bootstrap percolation, the {Schr\"{o}der} numbers, and the $n$-kings
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\newblock \emph{SIAM Journal on Discrete Mathematics} \textbf{4} (1991),
  275--280.

\bibitem[{Sloane(2006)}]{sloane}
N.~J.~A. Sloane.
\newblock The on-line encyclopedia of integer sequences, 2006.

\bibitem[{Uno and Yagiura(2000)}]{UnoYag00}
Takeaki Uno and Mutsunori Yagiura.
\newblock Fast algorithms to enumerate all common intervals of two
  permutations.
\newblock \emph{Algorithmica} \textbf{26} (2000), 290--309.

\bibitem[{Wolfowitz(1944)}]{Wolfowitz44}
J.~Wolfowitz.
\newblock Note on runs of consecutive elements.
\newblock \emph{Annals of Mathematical Statistics} \textbf{15} (1944), 97--98.

\bibitem[{Wu(1997)}]{DekaiCL}
Dekai Wu.
\newblock Stochastic inversion transduction grammars and bilingual parsing of
  parallel corpora.
\newblock \emph{Computational Linguistics} \textbf{23} (1997), 377--403.

\bibitem[{Zhang and Gildea(2006)}]{Zhang-gildea-tr06}
Hao Zhang and Daniel Gildea.
\newblock Efficient factorization of synchronous context-free grammars.
\newblock Technical Report 889, University of Rochester, 2006.

\bibitem[{Zhang et~al.(2006)Zhang, Huang, Gildea, and Knight}]{ZHGK-naacl06}
Hao Zhang, Liang Huang, Daniel Gildea, and Kevin Knight.
\newblock Synchronous binarization for machine translation.
\newblock In \emph{Proceedings of the Human Language Technology
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\end{thebibliography}