\def\cprime{$'$}
\begin{thebibliography}{100}

\bibitem{AgMe77}
{\sc Agrawal, G.~P., and Mehta, C.~L.}
\newblock Ordering of the exponential of a quadratic in boson operators.
  {II}.~{M}ultimode case.
\newblock {\em Journal of Mathematical Physics 18}, 3 (1977), 408--412.

\bibitem{AtNe72}
{\sc Athreya, K.~B., and Ney, P.~E.}
\newblock {\em Branching processes}.
\newblock Springer-Verlag, New York, 1972.
\newblock Die Grundlehren der mathematischen Wissenschaften, Band 196.

\bibitem{BaDo01}
{\sc Baez, J.~C., and Dolan, J.}
\newblock From finite sets to {F}eynman diagrams.
\newblock In {\em Mathematics Unlimited---2001 and Beyond}, B.~Engquist and
  W.~Schmid, Eds. Springer, Berlin, 2001, pp.~29--50.

\bibitem{BaFl02}
{\sc Banderier, C., and Flajolet, P.}
\newblock Basic analytic combinatorics of directed lattice paths.
\newblock {\em Theoretical Computer Science 281}, 1-2 (2002), 37--80.

\bibitem{BeBrMe99}
{\sc Bender, C.~M., Brody, D.~C., and Meister, B.~K.}
\newblock Quantum field theory of partitions.
\newblock {\em Journal of Mathematical Physics 40}, 7 (1999), 3239--3245.

\bibitem{BeFlSa92}
{\sc Bergeron, F., Flajolet, P., and Salvy, B.}
\newblock Varieties of increasing trees.
\newblock In {\em CAAP'92\/} (1992), J.-C. Raoult, Ed., vol.~581 of {\em
  Lecture Notes in Computer Science}, pp.~24--48.
\newblock Proceedings of the 17th Colloquium on Trees in Algebra and
  Programming, Rennes, France, February 1992.

\bibitem{BeLaLe98}
{\sc Bergeron, F., Labelle, G., and Leroux, P.}
\newblock {\em Combinatorial species and tree-like structures}.
\newblock Cambridge University Press, 1998.

\bibitem{Berndt89}
{\sc Berndt, B.~C.}
\newblock {\em Ramanujan's Notebooks, Part {II}}.
\newblock Springer Verlag, 1989.

\bibitem{Biggs74}
{\sc Biggs, N.~L.}
\newblock {\em Algebraic Graph Theory}.
\newblock Cambridge University Press, 1974.

\bibitem{Blasiak05}
{\sc Blasiak, P.}
\newblock {\em Combinatorics of boson normal ordering and some applications}.
\newblock PhD thesis, University Pierre \& Marie Curie (Paris) and Institute of
  Nuclear Physics of Polish Academy of Sciences, Krak\'ow, 2005.

\bibitem{Blasiak10b}
{\sc Blasiak, P.}
\newblock On urn models, non-commutativity and operator normal forms.
\newblock {\em Physics Letters {A} 374\/} (2010), 4808--4813.

\bibitem{BlDaHoPe06}
{\sc Blasiak, P., Dattoli, G., Horzela, A., and Penson, K.~A.}
\newblock Representations of monomiality principle with sheffer-type
  polynomials and boson normal ordering.
\newblock {\em Physics Letters A 352\/} (2006), 7--12.

\bibitem{BlDuHoPeSo08}
{\sc Blasiak, P., Duchamp, G. H.~E., Horzela, A., Penson, K.~A., and Solomon,
  A.~I.}
\newblock {Heisenberg--Weyl} algebra revisited: Combinatorics of words and
  paths.
\newblock {\em Journal of Physics~A: Mathematical and Theoretical 41}, 415204
  (2008), 1--8.

\bibitem{BlDuSoHoPe10}
{\sc Blasiak, P., Duchamp, G. H.~E., Solomon, A.~I., Horzela, A., and Penson,
  K.~A.}
\newblock Combinatorial algebra for second-quantized quqntum theory.
\newblock {\em Advances in Theoretical and Mathematical Physics 14}, 4 (2010).
\newblock In press. Also available as {\tt arXiv:1001.4964 [math-ph]}.

\bibitem{BlHoPeSo06}
{\sc Blasiak, P., Horzela, A., Penson, K., and Solomon, I.}
\newblock Dobi{\'n}ski-type relations: some properties and physical
  applications.
\newblock {\em Journal of Physics A: Math. Gen. 39\/} (2006), 4999--5006.

\bibitem{BlHoPeDuSo05}
{\sc Blasiak, P., Horzela, A., Penson, K.~A., Duchamp, G. H.~E., and Solomon,
  A.~I.}
\newblock Boson normal ordering via substitutions and {Sheffer}-type
  polynomials.
\newblock {\em Physics Letters~{A} 338\/} (2005), 108.

\bibitem{BlHoPeSoDu07}
{\sc Blasiak, P., Horzela, A., Penson, K.~A., Solomon, A.~I., and Duchamp, G.
  H.~E.}
\newblock Combinatorics and boson normal ordering: {A} gentle introduction.
\newblock {\em American Journal of Physics 75}, 7 (2007), 639--646.
\newblock {\tt arXiv:0704.3116v1 [quant-ph]}, 8 pages.

\bibitem{BlPeSo03}
{\sc Blasiak, P., Penson, K.~A., and Solomon, A.~I.}
\newblock Dobi{\'n}ski-type relations and the log-normal distribution.
\newblock {\em Journal of Physics {A}: Mathematical and General 36\/} (2003),
  L273--L278.

\bibitem{BlPeSo03b}
{\sc Blasiak, P., Penson, K.~A., and Solomon, A.~I.}
\newblock The general boson normal ordering problem.
\newblock {\em Physics Letters~{A} 309\/} (2003), 198--205.

\bibitem{Bollobas85}
{\sc Bollob{\'a}s, B.}
\newblock {\em Random Graphs}.
\newblock Academic Press, 1985.

\bibitem{BrCoEsPaRe06}
{\sc Brak, R., Corteel, S., Essam, J., Parviainen, R., and Rechnizter, A.}
\newblock A combinatorial derivation of the {PASEP} stationary state.
\newblock {\em The Electronic Journal of Combinatorics 13}, R108 (2006), 1--23.

\bibitem{BrItPaZu78}
{\sc Br{\'e}zin, {\'E}., Itzykson, C., Parisi, G., and Zuber, J.-B.}
\newblock Planar diagrams.
\newblock {\em Communications in Mathematical Physics 59\/} (1978), 35--51.

\bibitem{CaSc74}
{\sc Carlitz, L., and Scoville, R.}
\newblock Generalized {Eulerian } numbers: combinatorial applications.
\newblock {\em Journal f{\"u}r die reine und angewandte Mathematik 265\/}
  (1974), 110--137.

\bibitem{Chapuy09}
{\sc Chapuy, G.}
\newblock Asymptotic enumeration of constellations and related families of maps
  on orientable surfaces.
\newblock {\em Combinatorics, Probability and Computing 18\/} (2009), 477--516.

\bibitem{Comtet74}
{\sc Comtet, L.}
\newblock {\em Advanced Combinatorics}.
\newblock Reidel, 1974.

\bibitem{Conrad02}
{\sc Conrad, E. v.~F.}
\newblock {\em Some Continued Fraction Expansions of {L}aplace Transforms of
  Elliptic Functions}.
\newblock {PhD Thesis}, The Ohio State University, 2002.

\bibitem{CoFl06}
{\sc Conrad, E. v.~F., and Flajolet, P.}
\newblock The {Fermat} cubic, elliptic functions, continued fractions, and a
  combinatorial excursion.
\newblock {\em S\'eminaire Lotharingien de Combinatoire 54}, B54g (2006),
  1--44.

\bibitem{CoJoPrRu09}
{\sc Corteel, S., Josuat-Verg\`es, M., Prellberg, T., and Rubey, M.}
\newblock Matrix {Ansatz}, lattice paths and rook placements.
\newblock In {\em Proceedings of FPSAC 2009, Hagenberg, Austria\/} (2009),
  vol.~{AK} of {\em DMTCS Proceedings}, pp.~313--324.

\bibitem{DasGupta96}
{\sc DasGupta, A.}
\newblock Disentanglement formulas: {An} alternative derivatin and some
  applications to squeezed coherent states.
\newblock {\em American Journal of Physics 64}, 11 (1996), 1422--1427.

\bibitem{Dattoli97}
{\sc Dattoli, G., Ottaviani, P.~L., Torre, A., and V{\'a}zquez, L.}
\newblock Evolution operator equations: integration with algebraic and
  finite-difference methods. applications to physical problems in classical and
  quantum mechanics and quantum field theory.
\newblock {\em Rivista del Nuovo Cimento 20}, 2 (1997), 1--133.

\bibitem{DaBa62}
{\sc David, F.~N., and Barton, D.~E.}
\newblock {\em Combinatorial Chance}.
\newblock Charles Griffin, 1962.

\bibitem{DeEvHaPa93}
{\sc Derrida, B., Evans, M.~R., V., H., and V., P.}
\newblock Exact solution of a $1d$ asymmetric exclusion model using a matrix
  formulation.
\newblock {\em Journal of Physics A: Mathematical and General 26}, 7 (1993),
  1493--1517.

\bibitem{Diestel00}
{\sc Diestel, R.}
\newblock {\em Graph Theory}.
\newblock No.~173 in Graduate Texts in Mathematics. Springer Verlag, 2000.

\bibitem{Duchon00}
{\sc Duchon, P.}
\newblock On the enumeration and generation of generalized {D}yck words.
\newblock {\em Discrete Mathematics 225}, 1-3 (2000), 121--135.
\newblock Formal power series and algebraic combinatorics (Toronto, ON, 1998).

\bibitem{DuFlRoTa07}
{\sc Dumas, V., Flajolet, P., Robert, P., and Tauraso, R.}
\newblock Coupon collection with group drawings.
\newblock Unpublished memoir, 2007.
\newblock 9 pages.

\bibitem{Dumont86}
{\sc Dumont, D.}
\newblock Pics de cycles et d\'eriv\'ees partielles.
\newblock {\em S\'eminaire Lotharingien de Combinatoire 37}, Art. B13a (1986),
  1--19.

\bibitem{Dumont96}
{\sc Dumont, D.}
\newblock Grammaires de {W}illiam {C}hen et d\'erivations dans les arbres et
  arborescences.
\newblock {\em S\'eminaire Lotharingien de Combinatoire 37}, Art. B37a (1996),
  1--21.

\bibitem{DyMK72}
{\sc Dym, H., and McKean, H.~P.}
\newblock {\em {F}ourier Series and Integrals}.
\newblock Academic Press, 1972.

\bibitem{EdKo94}
{\sc Edelman, A., and Kostlan, E.}
\newblock The road from {K}ac's matrix to {K}ac's random polynomials.
\newblock In {\em Proceedings of the 1994 SIAM Applied Linear Algebra
  Conference\/} (Philadelphia, 1994), J.~Lewis, Ed., SIAM, pp.~503--507.

\bibitem{EhEh07}
{\sc Ehrenfest, P., and Ehrenfest, T.}
\newblock {\"U}ber zwei bekannte {E}inw{\"a}nde gegen das {B}oltzmannsche
  {$H$-Theorem}.
\newblock {\em Physikalische Zeitschrift 8}, 9 (1907), 311--314.

\bibitem{EnNa00}
{\sc Engel, K.-J., and Nagel, R.}
\newblock {\em One-Parameter Semigroups for Linear Evolution Equations},
  vol.~194 of {\em Graduate Texts in Mathematics}.
\newblock Springer Verlag, 2000.

\bibitem{Feller68}
{\sc Feller, W.}
\newblock {\em An Introduction to Probability Theory and its Applications},
  third~ed., vol.~1.
\newblock John Wiley, 1968.

\bibitem{Feynman62}
{\sc Feynman, R.~P.}
\newblock {\em Quantum Eletrodynamics}.
\newblock Benjamin, 1962.

\bibitem{Feynman88}
{\sc Feynman, R.~P.}
\newblock {\em {QED} The Strange Theory of Light and Matter}.
\newblock Princeton University Press, 1988.

\bibitem{Flajolet80b}
{\sc Flajolet, P.}
\newblock Combinatorial aspects of continued fractions.
\newblock {\em Discrete Mathematics 32\/} (1980), 125--161.
\newblock Reprinted in the 35th Special Anniversary Issue of \emph{Discrete
  Mathematics}, Volume 306, Issue 10--11, Pages 992-1021 (2006).

\bibitem{FlDuPu06}
{\sc Flajolet, P., Dumas, P., and Puyhaubert, V.}
\newblock Some exactly solvable models of urn process theory.
\newblock {\em Discrete Mathematics \& Theoretical Computer Science
  (Proceedings) AG\/} (2006), 59--118.

\bibitem{FlGaPe05}
{\sc Flajolet, P., {Gabarr\'o}, J., and Pekari, H.}
\newblock Analytic urns.
\newblock {\em Annals of Probability 33}, 3 (2005), 1200--1233.

\bibitem{FlHu08}
{\sc Flajolet, P., and Huillet, T.}
\newblock Analytic combinatorics of the {M}abinogion urn.
\newblock In {\em Proceedings of Fifth Colloquium on Mathematics and Computer
  Science: Algorithms, Trees, Combinatorics and Probabilities\/} (Blaubeuren,
  2008), U.~R{\"o}sler, Ed., vol.~AI of {\em Discrete Mathematics and
  Theoretical Computer Science Proceedings}, pp.~549--572.

\bibitem{FlNo00}
{\sc Flajolet, P., and Noy, M.}
\newblock Analytic combinatorics of chord diagrams.
\newblock In {\em Formal Power Series and Algebraic Combinatorics\/} (2000),
  A.~V.~M. D.~Krob, A. A.~Mikhalev, Ed., Springer, pp.~191--201.
\newblock (Proceedings of the 12th International Conference, FPSAC'2000; June
  2000, Moscow.).

\bibitem{FlPuVu86}
{\sc Flajolet, P., Puech, C., and Vuillemin, J.}
\newblock The analysis of simple list structures.
\newblock {\em Information Sciences 38\/} (1986), 121--146.

\bibitem{FlSe09}
{\sc Flajolet, P., and Sedgewick, R.}
\newblock {\em Analytic Combinatorics}.
\newblock Cambridge University Press, 2009.
\newblock 824 pages. Also available electronically from the authors' home
  pages.

\bibitem{Fomin88}
{\sc Fomin, S.~V.}
\newblock Generalized {Robinson--Schensted--Knuth} correspondence.
\newblock {\em Journal of Soviet Mathematics 41}, 2 (1988), 979--991.

\bibitem{Fomin94}
{\sc Fomin, S.~V.}
\newblock Duality of graded graphs.
\newblock {\em Journal of Algebraic Combinatorics 3}, 4 (1994), 357--404.

\bibitem{Fomin95}
{\sc Fomin, S.~V.}
\newblock Schensted algorithms for dual graded graphs.
\newblock {\em Journal of Algebraic Combinatorics 4}, 1 (1995), 5--45.

\bibitem{FrVi79}
{\sc Fran{\c c}on, J., and Viennot, G.}
\newblock Permutations selon leurs pics, creux, doubles mont{\'e}es et doubles
  descentes, nombres d'{E}uler et de {G}enocchi.
\newblock {\em Discrete Mathematics 28\/} (1979), 21--35.

\bibitem{Friedman49}
{\sc Friedman, B.}
\newblock A simple urn model.
\newblock {\em Communications in Pure and Applied Mathematics 2\/} (1949),
  59--70.

\bibitem{Friedrichs65}
{\sc Friedrichs, K.~O.}
\newblock {\em Perturbation of spectra in {Hilbert Space}}, vol.~3 of {\em
  Lectures in Applied Mathematics}.
\newblock American Mathematical Society, 1965.

\bibitem{Gilmore74}
{\sc Gilmore, R.}
\newblock {\em Lie Groups, {Lie} Algebras, and some of their Applications}.
\newblock Wiley, 1974.

\bibitem{GoJa83}
{\sc Goulden, I.~P., and Jackson, D.~M.}
\newblock {\em Combinatorial Enumeration}.
\newblock John Wiley, New York, 1983.

\bibitem{GoJa86}
{\sc Goulden, I.~P., and Jackson, D.~M.}
\newblock Distributions, continued fractions, and the {E}hrenfest urn model.
\newblock {\em Journal of Combinatorial Theory. Series A 41}, 1 (1986), 21--31.

\bibitem{GrKnPa89}
{\sc Graham, R.~L., Knuth, D.~E., and Patashnik, O.}
\newblock {\em Concrete Mathematics}.
\newblock Addison Wesley, 1989.

\bibitem{Greene83}
{\sc Greene, D.~H.}
\newblock {\em Labelled formal languages and their uses}.
\newblock {Ph.D. Thesis}, Stanford University, June 1983.
\newblock Available as Report STAN-CS-83-982.

\bibitem{GrKn90}
{\sc Greene, D.~H., and Knuth, D.~E.}
\newblock {\em Mathematics for the analysis of algorithms}, third~ed.
\newblock Birkhauser, Boston, 1990.

\bibitem{Hall03}
{\sc Hall, B.~C.}
\newblock {\em Lie Groups, {Lie} Algebras, and Representations}.
\newblock No.~222 in Graduate Texts in Mathematics. Springer Verlag, 2003.

\bibitem{HeLo65}
{\sc Heffner, H., and Louisell, W.~H.}
\newblock Transformation having applications in quantum mechanics.
\newblock {\em Journal of Mathematical Physics 6}, 3 (1965), 474--478.

\bibitem{HoSu07}
{\sc Hodges, A., and Sukumar, C.}
\newblock Bernoulli, {E}uler, permutations and quantum algebras.
\newblock {\em Proceedings of the Royal Society A 463\/} (2007), 2401--2414.

\bibitem{JaLoMa10}
{\sc Janson, S., Louchard, G., and Martin-L\"of, A.}
\newblock The maximum of {Brownian} motion with parabolic drift ({Extended}
  abstract).
\newblock In {\em {AofA'10 (Analysis of Algorithms)}\/} (2010), vol.~{AM} of
  {\em Discrete Mathematics and Theoretical Computer Science (DMTCS)
  Proceedings}, pp.~427--438.

\bibitem{JoKo77}
{\sc Johnson, N.~L., and Kotz, S.}
\newblock {\em Urn Models and Their Application}.
\newblock John Wiley, 1977.

\bibitem{Johnson02}
{\sc Johnson, W.~P.}
\newblock The curious history of {Fa\`a} di {Bruno}'s formula.
\newblock {\em The American Mathematical Monthly 109\/} (March 2002), 217--234.

\bibitem{Jordan65}
{\sc Jordan, C.}
\newblock {\em Calculus of Finite Differences}.
\newblock Chelsea Publishing Company, 1965.
\newblock First Edition, Budapest, 1939.

\bibitem{Josuat09b}
{\sc Josuat-Verg\`es, M.}
\newblock Matrix {Ansatz} and enumeration of crossings.
\newblock Seminar at LIX, \'Ecole Polytechnique, May 2009.
\newblock Slides available from the author's web pages.

\bibitem{Josuat09c}
{\sc Josuat-Verg\`es, M.}
\newblock Rook placements in {Young} diagrams and permutation enumeration.
\newblock Submitted, 2009.

\bibitem{Josuat10}
{\sc Josuat-Verg\`es, M.}
\newblock A $q$-enumeration of alternating permutations.
\newblock {\em European Journal of Combinatorics 31}, 7 (2010), 1689--1705.

\bibitem{Joyal81}
{\sc Joyal, A.}
\newblock Une th{\'e}orie combinatoire des s{\'e}ries formelles.
\newblock {\em Advances in Mathematics 42}, 1 (1981), 1--82.

\bibitem{Kac47}
{\sc Kac, M.}
\newblock Random walk and the theory of {B}rownian motion.
\newblock {\em American Mathematical Monthly 54\/} (1947), 369--391.

\bibitem{KaCh02}
{\sc Kac, V., and Cheung, P.}
\newblock {\em Quantum Calculus}.
\newblock Universitext. Springer, 2002.

\bibitem{Katriel74}
{\sc Katriel, J.}
\newblock Combinatorial aspects of boson algebra.
\newblock {\em Lettere al Nuovo Cimento 10}, 13 (1974), 565--567.

\bibitem{Katriel83}
{\sc Katriel, J.}
\newblock Normal ordering formulae for some boson operators.
\newblock {\em Journal of Physics {A}: Mathematical and General 16\/} (1983),
  4171--4173.

\bibitem{Katriel00}
{\sc Katriel, J.}
\newblock Bell numbers and coherent states.
\newblock {\em Physics Letters {A} 273\/} (2000), 159--161.

\bibitem{Katriel02}
{\sc Katriel, J.}
\newblock Coherent states and combinatorics.
\newblock {\em Journal of Optics B: Quantum Semiclassical Optics 4\/} (2002),
  S200--S203.

\bibitem{KaDu95}
{\sc Katriel, J., and Duchamp, G.}
\newblock Ordering relations for $q$--boson operators, continued fraction
  techniques and the $q$--cbh enigma.
\newblock {\em Journal of Physics {A}: Mathematical and General 28\/} (1995),
  7209--7225.

\bibitem{KaKi92}
{\sc Katriel, J., and Kibler, M.}
\newblock Normal ordering for deformed boson operators and operator-valued
  deformed {Stirling} numbers.
\newblock {\em Journal of Physics {A}: Mathematical and General 24\/} (1992),
  2683--2691.

\bibitem{KaSo91}
{\sc Katriel, J., and Solomon, A.~I.}
\newblock Generalized $q$--bosons and their squeezed states.
\newblock {\em Journal of Physics {A}: Mathematical and General 24\/} (1991),
  2093--2105.

\bibitem{Lang00}
{\sc Lang, W.}
\newblock On generalizations of the stirling number triangles.
\newblock {\em Journal of Integer Sequences 3}, 2.4 (2000), 1--19.

\bibitem{Lang09}
{\sc Lang, W.}
\newblock Combinatorial interpretation of generalized stirling numbers.
\newblock {\em Journal of Integer Sequences 12}, 3 (2009), 1--26.

\bibitem{LeVi86}
{\sc Leroux, P., and Viennot, G.~X.}
\newblock Combinatorial resolution of systems of differential equations {I:}
  {O}rdinary differential equations.
\newblock In {\em Combinatoire {\'E}num\'erative\/} (1986), G.~Labelle and
  P.~Leroux, Eds., no.~1234 in Lecture Notes in Mathematics, Springer-Verlag,
  pp.~210--245.

\bibitem{LeVi88b}
{\sc Leroux, P., and Viennot, X.~G.}
\newblock Combinatorial resolution of systems of differential equations. {IV:}
  {S}eparation of variables.
\newblock {\em Discrete Mathematics 72\/} (1988), 237--250.

\bibitem{Louchard87b}
{\sc Louchard, G.}
\newblock Random walks, {G}aussian processes and list structures.
\newblock {\em Theoretical Computer Science 53}, 1 (1987), 99--124.

\bibitem{Louisell90}
{\sc Louisell, W.~H.}
\newblock {\em Quantum Statistical Properties of Radiation}.
\newblock Wiley, 1990.
\newblock Wiley Classic Library Edition. A reprint of the 1973 original.

\bibitem{Mahmoud03}
{\sc Mahmoud, H.}
\newblock Urn models and connections to random trees: a review.
\newblock {\em Journal of the Iranian Mathematical Society 2\/} (2003),
  53--114.

\bibitem{Mahmoud08}
{\sc Mahmoud, H.~M.}
\newblock {\em {P\'olya} Urn Models}.
\newblock CRC Texts in Statistical Science Series. Chapman \& Hall, 2008.

\bibitem{MaScSe07}
{\sc Mansour, T., Schork, M., and Severini, S.}
\newblock Wick's theorem for $q$--deformed boson operators.
\newblock {\em Journal of Physics {A}: Mathematical and General 40\/} (2007),
  8393--8401.

\bibitem{Marburger66}
{\sc Marburger, J.~H.}
\newblock Conditions for the existence of closed solutions by the normal
  ordering method.
\newblock {\em Journal of Mathematical Physics 7}, 5 (1966), 829--832.

\bibitem{Marburger67}
{\sc Marburger, J.~H.}
\newblock Relation of normal-ordring methods to linked diagrams.
\newblock {\em Physical Review 158}, 5 (1967), 1557--1660.

\bibitem{Mattuck92}
{\sc Mattuck, R.~D.}
\newblock {\em A guide to {Feynman} diagrams in the many-body problem}.
\newblock Dover Publications, 1992.

\bibitem{Mehta77}
{\sc Mehta, C.~L.}
\newblock Ordering of the exponential of a quadratic in boson operators.
  {I}.~{S}ingle mode case.
\newblock {\em Journal of Mathematical Physics 18}, 3 (1977), 404--407.

\bibitem{MeRo08b}
{\sc M\'endez, M., and Rodr\'iguez, A.}
\newblock A combinatorial model for $q$-generalized {Stirling and Bell}
  numbers.
\newblock In {\em Formal Power Series and Algebraic Combinatorics (FPSAC 2008,
  Valparaiso)\/} (2008), vol.~AJ of {\em DMTCS Proceedings}, pp.~557--570.

\bibitem{MeRo08}
{\sc M\'endez, M., and Rodriguez, A.}
\newblock $q$-analogs of the generalized {Stirling and Bell} numbers.
\newblock In {\em Symmetry and Structural Properties of Condensed Matter\/}
  (2008), vol.~104 of {\em Journal of Physics: Conference Series}, pp.~1--10.

\bibitem{MeBlPe05}
{\sc M{\'e}ndez, M.~A., Blasiak, P., and Penson, K.~A.}
\newblock Combinatorial approach to generalized {Bell} and {Stirling} numbers
  and boson normal ordering problem.
\newblock {\em Journal of Mathematical Physics 46}, 083511 (2005), 1--8.
\newblock Available as arXiv:quant-ph/0505180.

\bibitem{Mikhailov83}
{\sc Mikhailov, V.~V.}
\newblock Ordering of some boson operator functions.
\newblock {\em Journal of Physics {A}: Mathematical and General 16\/} (1983),
  3817--3827.

\bibitem{Mikhailov85}
{\sc Mikhailov, V.~V.}
\newblock Normal ordering and generalised {Stirling} numbers.
\newblock {\em Journal of Physics {A}: Mathematical and General 18\/} (1985),
  231--235.

\bibitem{Milne81}
{\sc Milne-Thomson, L.~M.}
\newblock {\em The Calculus of Finite Differences}.
\newblock Chelsea Publishing Company, 1981.
\newblock Reprinted from the original edition, London, 1933.

\bibitem{Noori10}
{\sc Mohammad-Noori, M.}
\newblock Some remarks about the derivation operator and generalized {Stirling}
  numbers.
\newblock Technical report, Department of Mathematics, Statistics and Computer
  Science, University of Tehran, 2010.
\newblock 16 pages.

\bibitem{PaPr98b}
{\sc Panholzer, A., and Prodinger, H.}
\newblock An analytic approach for the analysis of rotations in fringe-balanced
  binary search trees.
\newblock {\em Annals of Combinatorics 2\/} (1998), 173--184.

\bibitem{Perron57}
{\sc Perron, O.}
\newblock {\em Die {L}ehre von den {K}ettenbr{\"u}chen}, vol.~2.
\newblock Teubner, 1957.

\bibitem{Prodinger08}
{\sc Prodinger, H.}
\newblock A continued fraction expansion for a $q$-tangent function: an
  elementary proof.
\newblock {\em S{\'e}minaire Lotharingien de Combinatoire, B60b (2008), 3 pp.
  60}, B60b (2008), 1--3.

\bibitem{Prodinger10}
{\sc Prodinger, H.}
\newblock Continued fraction expansions for $q$-tangent and $q$-cotangent
  functions.
\newblock {\em Discrete Mathematics \& Theoretical Computer Science 12}, 2
  (2010).

\bibitem{Read79}
{\sc Read, R.~C.}
\newblock The chord intersection problem.
\newblock {\em Annals of the New York Academy of Sciences 319\/} (May 1979),
  444--454.

\bibitem{Riordan68}
{\sc Riordan, J.}
\newblock {\em Combinatorial Identities}.
\newblock Wiley, 1968.

\bibitem{Riordan75}
{\sc Riordan, J.}
\newblock The distribution of crossings of chords joining pairs of $2n$ points
  on a circle.
\newblock {\em Mathematics of Computation 29}, 129 (1975), 215--222.

\bibitem{Riordan80}
{\sc Riordan, J.}
\newblock {\em An {I}ntroduction to {C}ombinatorial {A}nalysis}.
\newblock Princeton University Press, Princeton, 1980.

\bibitem{Ritt50}
{\sc Ritt, J.~F.}
\newblock {\em Differential Algebra}, vol.~XXXIII of {\em A.M.S. Colloquium}.
\newblock A.M.S., 1950.

\bibitem{Scherk23}
{\sc Scherk, H.~F.}
\newblock {\em De evolvenda functione $(yd.yd.yd...ydX/dx^n)$ disquisitiones
  nonnullae analyticae}.
\newblock PhD thesis, Berlin, 1823.
\newblock Publicly available from G\"ottinger Digitalisierungszentrum (GDZ).

\bibitem{Schork03}
{\sc Schork, M.}
\newblock On the combinatorics of normal ordering bosonic operators and
  deformations of it.
\newblock {\em Journal of Physics {A}: Mathematical and General 36\/} (2003),
  4651--4665.

\bibitem{ShZe10}
{\sc Shin, H., and Zeng, J.}
\newblock The $q$-tangent and $q$-secant numbers via continued fractions.
\newblock {\em European Journal of Combinatorics 31}, 7 (2010), 1689--1705.

\bibitem{Sloane08}
{\sc Sloane, N. J.~A.}
\newblock {\em {The On-Line Encyclopedia of Integer Sequences}}.
\newblock 2008.
\newblock Published electronically at {\tt
  www.research.att.com/\~{}njas/sequences/}.

\bibitem{SoDuBlHoPe04}
{\sc Solomon, A.~I., Duchamp, G. H.~E., Blasiak, P., and Penson, K.~A.}
\newblock Normal order: Combinatorial graphs.
\newblock In {\em Quantum Theory and Symmetries\/} (2004), World Scientific,
  pp.~398--406.

\bibitem{Stadje90}
{\sc Stadje, W.}
\newblock The collector's problem with group drawings.
\newblock {\em Advances in Applied Probability 22}, 4 (1990), 866--822.

\bibitem{Stanley86}
{\sc Stanley, R.~P.}
\newblock {\em Enumerative Combinatorics}, vol.~I.
\newblock Wadsworth \& Brooks/Cole, 1986.

\bibitem{Stanley88}
{\sc Stanley, R.~P.}
\newblock Differential posets.
\newblock {\em Journal of the American Mathematical Society 1}, 4 (1988),
  919--961.

\bibitem{Stanley90}
{\sc Stanley, R.~P.}
\newblock Variations on differential posets.
\newblock In {\em {Invariant theory and tableaux ({M}inneapolis, {MN}, 1988)}},
  vol.~19 of {\em IMA Vol. Math. Appl.} Springer, New York, 1990, pp.~145--165.

\bibitem{Stanley99}
{\sc Stanley, R.~P.}
\newblock {\em Enumerative Combinatorics}, vol.~II.
\newblock Cambridge University Press, 1999.

\bibitem{SuHo07}
{\sc Sukumar, C., and Hodges, A.}
\newblock Quantum algebras and parity-dependent spectra.
\newblock {\em Proceedings of the Royal Society A 463\/} (2007), 2415---2427.

\bibitem{Taylor96}
{\sc Taylor, M.~E.}
\newblock {\em Partial differential equations. {I}}, vol.~115 of {\em Applied
  Mathematical Sciences}.
\newblock Springer-Verlag, New York, 1996.

\bibitem{Touchard52}
{\sc Touchard, J.}
\newblock Sur un probl{\`e}me de configuration et sur les fractions continues.
\newblock {\em Canadian Journal of Mathematics 4\/} (1952), 2--25.

\bibitem{Poorten79}
{\sc van~der Poorten, A.}
\newblock A proof that {E}uler missed {$\ldots$} {Ap\'ery}'s proof of the
  irrationality of {$\zeta(3)$}.
\newblock {\em Mathematical Intelligencer 1\/} (1979), 195--203.

\bibitem{Varvak05}
{\sc Varvak, A.}
\newblock Rook numbers and the normal ordering problem.
\newblock {\em Journal of Combinatorial Theory, Series~A 112}, 2 (2005),
  292--307.

\bibitem{Viennot80}
{\sc Viennot, G.}
\newblock Une interpretation combinatoire des coefficients des
  d{\'e}veloppements en s{\'e}rie enti{\`e}re des fonctions elliptiques de
  {J}acobi.
\newblock {\em Journal of Combinatorial Theory, series A 29\/} (1980),
  121--133.

\bibitem{Viennot86}
{\sc Viennot, G.~X.}
\newblock Heaps of pieces, {I}: basic definitions and combinatorial lemmas.
\newblock In {\em Combinatoire {\'enum\'erative}\/} (1986), G.~Labelle and
  P.~Leroux, Eds., vol.~1234 of {\em Lecture Notes in Mathematics},
  Springer-Verlag, pp.~321--350.

\bibitem{Viennot09}
{\sc Viennot, X.~G.}
\newblock Catalan tableaux and the asymmetric exclusion process.
\newblock Tech. Rep.~{\tt arXiv:0905.3081}, ArXiv, 2009.

\bibitem{Wall48}
{\sc Wall, H.~S.}
\newblock {\em Analytic Theory of Continued Fractions}.
\newblock Chelsea Publishing Company, 1948.

\bibitem{Weinberg95a}
{\sc Weinberg, S.}
\newblock {\em The Quantum Theory of Fields -- Foundations}, vol.~{I}.
\newblock Cambridge University Press, 1995.

\bibitem{Wilcox67}
{\sc Wilcox, R.~M.}
\newblock Exponential operators and parameter differentiation in quantum
  physics.
\newblock {\em Jornal of Mathematical Physics 8}, 4 (1967), 962--982.

\bibitem{Wilf94}
{\sc Wilf, H.~S.}
\newblock {\em Generatingfunctionology}.
\newblock Academic Press, 1994.
\newblock Second edition, available on the internet from Herbert Wilf's home
  page.

\end{thebibliography}
