\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}