The Art of Bijective Combinatorics    Part IV
Combinatorial theory of orthogonal polynomials and continued fractions

The Institute of Mathematical Sciences, Chennai, India  (January-March 2019)

Some references

(list in progress)

Books on orthogonal polynomials (the classical point of view) (by chronogical order)

G.Szegö (1939). Orthogonal polynomials, Amer. Math. Soc. Colloquium Publi., vol.  XXIII, Providence, Rhode Island, 440 pp., reed. 1958,1966, 1975.
R. Askey (1975). Orthogonal polynomials and special functions, Society for Industrial and Applied Mathematics, Philadelphia,  vii+110 pp. 
T. Chihara (1978).  An introduction to orthogonal polynomials, Gordon and Breach, New-York,
reed. Dover Publications, Mineola, New-York, 2011, 156 pp.
G. Andrews, R. Askey and R. Roy (1999). Special functions, Encyclopedia of Mathematics and Applications, Vol 71,
Cambridge University Press, Cambridge U.K., 682 pp.
M. Ismail (2005). Classical and quantum orthogonal polynomials in one variable, Encyclopedia of Mathematics and Applications, Vol 98,
Cambridge University Press, Cambridge U.K., 726 pp.
S. Khrushchev (2008). Orthogonal polynomials and continued fractions from Euler's point of view, Encyclopedia of Mathematics and Applicqations, Vol 122,
Cambridge University Press, Cambridge U.K., 496 pp.
R. Koekoek, P.Lesky and R. Swarttow (2010). Hypergeometric orthogonal polynomials and their q-analogues, Springer Verlag, 578 pp.  

Books on continued fractions (the classical point of view)

H.S. Wall (1948).  Analytic Theory of Continued Fractions, Van Nostrand, New-York.
O. Perron (1954) Die  Lehre  von  den  Kettenbruchen, Band I,  Band I, Teubner, Stuttgart,
(1957) Die Lehre von den Kettenbruchen, Band II, Teubner, Stuttgart.
A.N. Khovanskii (1963) The Application of Continued Fractions and Their Generalizations to Problems in Approximation Theory  (translated by Peter Wynn),  
P. Noordhoff, Groningen, The Netherlands, first edition in Russian 1956
W. Jones and W. Thron (1980) (1984).  Continued fractions, analytic theory and applications, Encyclopedia of Mathematics and Applicqations, Vol 122,
Cambridge University Press, Cambridge U.K.

Monographs and Lecture Notes (the combinatorial point of view)

 X.G. Viennot (1983).  Une théorie combinatoire des polynômes orthogonaux généraux. Lecture Notes, UQAM, (Université du Québec à Montréal), 219 pp.  (pdf, 29Mo)
E. Roblet (1994). Une interprétation combinatoire des approximants de Padé, Publications du LACIM n°17, UQAM, Montréal, 213 pp.
A. Sokal, (2015), Coefficientwise total positivity (via continued fractions) for some Hankel matrices of combinatorial polynomials,manuscript 247pp, final version in preparation
summary in: talk at "Séminaire Philippe Flajolet", Institut Henri Poincaré, Paris, 5 June 2014; slides of the talk
J. Zeng (2016). Combinatorics of orthogonal polynomials and their moments, Lectures at the OPSF Summer School, University of Maryland, College Park, MD, July 11-July 15, 2
survey paper, with emphasis on the linearization coefficients of the Sheffer orthogonal polynomials, 48pp.

Articles related to the course

M. Anshelevich (2005). Linearization coefficients for orthogonal polynomials using stochastic processes. Ann. Probab. 33, no. 1, 114–136. 

M. Anshelevich (2005). A characterization of ultraspherical, Hermite and Chebyshev polynomials of the first kind, arXiv: 1108:0914 [math.CA]
R. Askey and M. E. H. Ismail (1976). Permutation problems and special functions. Canad. J. Math. 28, no. 4, 853–874. 

R. Askey, M. E. H. Ismail and T.Koorwinder (1978). Weighted permutations problems and Laguerre polynomials,  J. of Combinatorial Th. A,, 25, 277-287
R. Askey, M. E. H. Ismail and T. Rashed, (1975). A derangement problem, MRC Technical Report no1522. 
R. Askey and J. A. Wilson (1985). Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials. Mem. Amer. Math. Soc., 54 , no. 319, iv+55 pp. 

R. Azor, J. Gillis and J. D. Victor (1982). Combinatorial applications of Hermite polynomials. SIAM J. Math. Anal. 13 , no. 5, 879–890. 

M. Barnabei, F. Bonetti, M. Silimbanin (2011). Restricted involutions and Motzkin paths Advances in Applied Mathematics, 47, 102-115
P. Bary (2011). Riordan arrays, orthogonal polynomials as moments, and Hankel transforms, arXiv: 1102.0921 [math:CO].
P. Barry, M. D. Petkovic ́ and P. M. Rajkovic (2007). The Hankel transform of the sum of consecutive generalized Catalan numbers.
Integral Transform. Spec. Funct., 18:285- 296, 2007.

F. Bergeron (1990). Combinatoire des polynômes orthogonaux classiques: une approche unifiée, European  J. Combin. 11 , no. 5, 393–40 

P. Biane, Permutations suivant le type d’excédance et le nombre d’inversions et interprétation Combinatoire d’une fraction continue de Heine,
European J. Combin. 14 (1993), no. 4, 277-284.
P. Blasiak and P. Flajolet (2010/12). Combinatorial models of creation-annihilation. Sém. Lothar. Combin. 65 (2010/12), Art. B65c, 78 pp. 

R. A. Brualdi and S. Kirkland (2005). Aztec diamonds and digraphs, and Hankel determinants of Schr ̈oder numbers. J. Combin. Theory Ser. B, 94:334-351.
L. Carlitz (1978). A set of polynomials in three variables. Houston J. Math. 4, no. 1, 11–33. 

X. K. Chang, X. B. Hu and Y. N. Zhang (2013).  A direct method for evaluating some nice Hankel determinants and proofs of several conjectures.
Linear Algebra Appl., 4389:2523-2541.
F. Chapoton and J. Zeng (2015). Nombres de q-Bernoulli–Carlitz et fractions continues, to appear in J. Théor. Nombres de Bordeaux, arXiv:1507.04123. 

X. K. Chang,  X. B. Hu, H. Lei and Y. N. Yeh (2015). Combinatorial proofs of addition formulas, the Electronic Journal of Combinatorics 22 (2015), #P00
W. Y.C. Chen, N. Y. Li, L. W. Shapiro, and S. H.F. Yan (2007) Matrix identities on weighted partial Motzkin paths. European J. Combin., 28(4):1196-1207.
T. Chihara (1978). An introduction to orthogonal polynomials. Gordon and Breach, New York, London, 
Paris. 

J. Cigler and J. Zeng 
(2011). A curious q-analogue of Hermite polynomials. J. Combin. Theory Ser. A 118 , no. 1, 9–26. 

S. Corteel (2007). Crossings and alignments of permutations, Adv. in Appl. Math. 38 (2007), no. 2, 149– 163. 

S. Corteel, J.S. Kim and D. Stanton (2016). Moments of orthogonal polynomials and combinatorics,
Recent trends in combinatorics, 545–578, IMA Vol. Math. Appl., 159, Springer. 

R. J. Clarke, E. Steingrímssonn and J. Zeng (1997).  New Euler-Mahonian statistics on permutations and words. Adv. in Appl. Math. 18, no. 3, 237–270.
M. De Sainte-Catherine and X.G. Viennot (1985). Combinatorial interpretation of integrals of products of Hermite, Laguerre and Tchebycheff polynomials.
Polynomes Orthogonaux et Applications, C. Brezinski et aI., eds., (Bar-le-Duc, 1984), 120–128, Lecture Notes in Math. n°1171, Springer, Berlin.
A. De Médicis (1993). Aspects combinatoires des nombres de Stirling, des polynômes orthogo-naux de Sheffer et de leurs q-analogues,
Vol. 13, Publications du LACIM, UQAM, Montréal.
A. De Médicis (1998). The Combinatorics of Meixner Polynomials: Linearization Coefficients, Europ. J. Combinatorics, 19, 355–367.
A. De Médicis and D. Stanton (1996). Combinatorial orthogonal expansions, Proceedings of the American Mathematical Society, Vol. 124, no. 2, pp469-473
A. De Médicis, D. Stanton and D. White (1995). The combinatorics of q-Charlier polynomials. J. Combin. Theory Ser. A 69, no. 1, 87–114. 
A. de Médicis and X.G. Viennot (1994). Moments des q-polynômes de Laguerre et la bijection de Foata-Zeilberger, Advances in Applied Maths., 15, 262-304.
D. Dumont and J.Zeng (1998). Polynômes d'Euler et les fractions continues de Stieltjes--Rogers, Ramanujan J. 2, no. 3, 387--410. 
S. P. Eu, T. L. Wong and P. L. Yen (2012). Hankel determinants of sums of consecutive weighted Schröder numbers. Linear Algebra Appl., 437:2285-2299.
S. Even and J. Gillis (1976). Derangements and Laguerre polynomials. Math. Proc. Cambridge Philos. Soc. 79 ), no. 1, 135–143. 

P. Flajolet (1980). Combinatorial aspects of continued fractions. Discrete Math., 32), 125–161.
P. Flajolet, J. Françon and J. Vuillemin (1980). Sequence of operations analysis for dynamic data structures, J. Algorithms 1, 111–141.
P. Flajolet and R.Schott  (1990). Non-overlapping Partitions, Continued Fractions, Bessel Functions and  a Divergent Series, Europ. J.  Combinatorics, 11, 421-432. 
P. Flajolet and R. Sedgewick (2009).  Analytic combinatorics, Cambridge University Press, Cambridge, 

P. Flajolet and E. Van Fossen Conrad  (2006). The Fermat cubic, elliptic functions, continued fractions and a combinatorial excursion, 
Séminaire Lotharingien de Combinatoire volume 54, Article B54g, special issue, [Viennot Festschrift], Lucelle, April 2005—available electronically., 44p
D. Foata (1978). A combinatorial proof of the Mehler formula. J. Combin. Theory Ser. A 24, no. 3, 367–376. 

 D. Foata and V. Strehl (1981). Une extension multilinéaire de la formule d'Erdélyi pour les produits de fonctions hypergéométriques confluentes,
C.R. Acad. Sc. Paris, 293, p. 517-520. 
D. Foata (1981). Some Hermite polynomial identities and their combinatorics, Adv. Appl. Math. 2,  250–259.
D. Foata (1984). Combinatoire des identités sur les polynômes orthogonaux, Proc. Internat. Congress of Mathematics, Warsaw, Aug. 16–24, 1983,
Polish Scientific Publications and North-Holland, pp. 1541–1553.
D. Foata (2003). Une méthode combinatoire pour l'étude des fonctions spéciales,Journés sur les méthodes en mathématiques, Institut Henri Poincaré, Paris 2-3 avril 2003 
D. Foata (2010). Eulerian polynomials: from Euler’s time to the present. In The legacy of Alladi Ramakrishnan in the mathematical sciences.
Edited by Krishnaswami Alladi, John R. Klauder and Calyampudi R. Rao. Springer, New York, pp. 253–273. 

D. Foata and A. M. Garsia (1979). A combinatorial approach to the Mehler formulas for the Hermite polynomials, Relations between Combinatorics and other parts of Mathematics
(Proc. of Symposia in Pure Math., Ohio State Univ., Columbus, Ohio, 1978), vol. 34; D.K. Ray-Chaudhuri, Ed., Amer. Math. Soc., Providence, R.I., 163–179.
D. Foata and  G. N. Han (1994) Nombres de Fibonacci et polynômes orthogonaux, Leonardo Fibonacci: il tempo, le opere, l'ereditá scientifica
[Pisa. 23-25 Marzo 1994, Marcello Morelli e Marco Tangheroni, ed.], p. 179-200. Pisa, Pacini Editore (Fondazione IBM Italia). 
 D. Foata and J.  Labelle (1983). Modèles combinatoires pour les  polynomes de Meixner, Europ. J. Combin., 4 , 305-311.
D. Foata and P. Leroux (1983). Polynômes de Jacobi, interprétation combinatoire et fonction génératrice, Proc. Amer. Math. Soc. 87, 47–53.
D. Foata and M.-P. Schützenberger (1970). Théorie géométrique des polynômes eulériens. Lecture Notes in Mathematics, Vol. 138 Springer-Verlag, Berlin-New York.
D. Foata and V. Strehl (1981). Une extension multilinéaire de la formule d’Erdélyi pour les produits de fonctions hypergémétriques confluentes,
C. R. Acad. Sci. Paris 293 , 517–520.
D.Foata and V.Strehl (1984). Combinatorics of Laguerre Polynomials, Proceedings Waterloo Silver Jubilee Conference on Combinatorics, Waterloo 1982,
in: Enumeration and Design, (D. M. Jackson and S. A. Vanstone, eds.), Academic Press, 123-140. 
D. Foata and D. Zeilberger (1988). Laguerre polynomials, weighted derangements and positivity. SIAM J. Disc. Math. 1, 425–433. 

D. Foata and D. Zeilberger (1990). Denert’s permutation statistic is indeed Euler-Mahonian. Stud. Appl. Math. 83 , no. 1, 31–59. 

J. Françon (1978). Histoires de Fichiers, RAIRO Inf. Th. 12, 49–62.
J. Françon and X.G. Viennot (1979). Permutations selon leurs pics, creux, doubles montées et double descentes, nombres d’Euler et nombres de Genocchi.
Discrete Math. 28 , no1, 21–35.
A. Garsia and J. Remmel (1980) A combinatorial interpretation of q-derangement and q-Laguerre numbers, Europ. J. Combin. 1, 47–59.
I. Gessel (1989). Generalized rook polynomials and orthogonal polynomials, in: q-Series and Partitions, D. Stanton (ed.),
IMA Volumes in Mathematics and its Applications, vol. 18, Springer–Verlag.
I. Gessel and X.G. Viennot (1985). Binomial determinants, paths, and hook length formulae. Adv. in Math. 58 , no. 3, 300–321. 

I. Gessel (1989). Generalized rook polynomials and orthogonal polynomials. q-series and partitions (Minneapolis, MN, 1988), 159–176,
IMA Vol. Math. Appl., 18, Springer, New York. 

J. Gillis and G. Weiss (1960) Products of Laguerre polynomials. Math. Comput. 14, 60–63. 

J.Gillis, J. Jedwab and D.Zeilberger (1988). SIAM J. Math. Anal., 19(6), 1455–1461.
A Combinatorial Interpretation of the Integral of the Product of Legendre Polynomials
C. Godsil (1981). Hermite polynomials and a duality relation for the matching polynomial, Combinatorica, 1, 257-262.
C. Godsil (1993). Algebraic Combinatorics, Chapman and Hall, New York.
V. J. W. Guo, M. Ishikawa, H. Tagawa, Hiroyuki and J. Zeng (2015). A quadratic formula for basic hypergeometric series related to Askey-Wilson polynomials.
Proc. Amer. Math. Soc. 143, no. 
5, 2003–2015. 
P. Goulden and D. M. Jackson (2004). Combinatorial enumeration. With a foreword by Gian-Carlo Rota.
Reprint of the 1983 original. Dover Publications, Inc., Mineola, NY,
A. Hennessy (2011). A study of Riordan arrays with applications to continued fractions, orthogonal polynomials and lattice paths,
PhD Thesis, Waterford Institute of Technology.
G. Hetyei (2010). Meixner polynomials of the second kind and quantum algebras representing su(1,1), Proceedings of the Royal Society A 466, 1409-1428. 
M. Ismail, A. Kasraoui and J. Zeng (2013). Separation of variables and combinatorics of linearization coefficients of orthogonal polynomials.
J. Combin. Theory Ser. A 120, no. 3, 561–599. 

M. Ismail and D. Stanton (1998). More orthogonal polynomials as moments. Mathematical essays in honor of Gian-Carlo Rota (Cambridge, MA, 1996),
Progr. Math., vol. 161, Birkhäuser Boston, Boston, MA,  pp. 377–396. 

M. Ismail, D. Stanton and X.G. Viennot (1987). The combinatorics of q-Hermite polynomials and the Askey-Wilson integral. European J. Combin. 8, , 379–392. 

M. Ismail and J. Zeng (2010). Addition theorems via continued fractions. Trans. Amer. Math. Soc. 362 , no. 2, 957–983. 

M. Ismail and J. Zeng (2015). A combinatorial approach to the 2D-Hermite and 2D-Laguerre polynomials. Adv. in Appl. Math. 64  70–88. 

M. Josuat-Vergès (2011). Rook placements in Young diagrams and permutation enumeration. Adv. in  Appl. Math. 47, no. 1, 1–22. 

D. Jackson (1976). Laguerre polynomials and derangements, Math. Proc. Camb. Phil. Soc. 80, 213–214.
M. Josuat-Vergès (2014).  Enumeration of snakes and cycle-alternating permutations, Australas. J. Combin. 60, 279–305 (2014).
A. Joyal (1981). Une théorie combinatoire des séries formelles. Adv. in Math. 42 , no. 1, 1–82. 

I. Kaplansky (1944). Symbolic solution of certain problems in permutations, Bull. Amer. Math. Soc. 50,  906–914.
A. Kasraoui, D. Stanton, J. Zeng (2011). The combinatorics of Al-Salam–Chihara q-Laguerre polynomials. Adv. in Appl. Math. 47, no. 2, 216–239. 

A Kasraoui and J. Zeng (2006). Distribution of crossings, nestings and alignments of two edges in matchings and partitions. Electron. J. Combin. 13 (1),  R33. 

J. S. Kim and D. Stanton (2015). Bootstrapping and Askey-Wilson polynomials. J. Math. Anal. Appl. 421 (1)  501–520. 

D. Kim, D. Stanton and J. Zeng (2005/07). The combinatorics of the Al-Salam–Chahara q-Charlier polynomials. Sém. Lothar. Combin. 54 ), Art. B54i, 15 pp. 

D. Kim and J.Zeng (2000). On a continued fraction formula of Wall, Ramanujan J. 4 ), no. 4, 421--427. 
D. Kim and J.Zeng  (2001). A combinatorial formula for the linearization coefficients of general Sheffer polynomials, European J. Combin. 22 , no. 3, 313--332. 
C. Krattenthaler (1999). Advanced determinant calculus, Séminaire Lotharingien de Combinatoire (SLC 42), article B42q, 67pp.
G.  Kreweras (1981). Permutations partiellement soulignees et polynomes geometriques, Europ. J. Combin., 2, 151-163. 
G. Ksavrelof and J. Zeng (2002/04). Two involutions for signed excedance numbers. Sém. Lothar. Combin. 49 (2002/04), Art. B49e, 8 pp. 

J. Labelle and Y.N. Yeh (1987). A combinatorial model for Hahn polynomials, Seminaire Lotharingien de combinatoire XVI, Liebfraunberg (France),
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J. Labelle and Y.N. Yeh (1988). Some combinatorics of the hypergeometric series, Europ. J. Combin. 9, 593-605.
J. Labelle and Y.N. Yeh (1989). Combinatorial proofs of some limit formulas involving orthogonal polynomials. Discrete Mathematics 79, 77-93.

J. Labelle and Y.N. Yeh (1989). Combinatorial proofs of symmetry formulas for the generalized hypergeometric series.
Journal of Mathematical Analysis and Applications 139, 36-48.
 J. Labelle and Y.N. Yeh (1989). The combinatorics of Laguerre, Charlier, and Hermite polynomials. Studies in Applied Mathematics 80, 25-36.

P. Leroux and V. Strehl (1985). Jacobi-Polynomials: Combinatorics of the Basic Identities. Discrete Mathematics 57,167-187.
H. Liang, L. Mu and Y. Wang (2016). Catalan-like numbers and Stieltjes moment sequences. Discrete Math., 339(2):484-488.
Z. Lin, S. Fu (2017), On 1212-Avoiding Restricted Growth Functions. Electron. J. Combin. 24(1),  #P1.53. 

B. Nassrallah and M. Rahman, (1985). Projection formulas, a reproducing kernel and a generating function for q-Wilson polynomials. SIAM J. Math. Anal. 16 (1) 186–197. 
Q. Pan and J. Zeng (2019). Combinatorics of (q,y)-Laguerre polynomials and their moments, arXiv: 1901.00907 [math.C0].
M. Pétréolle, A. Sokal, Bao-Xuan Zhu (2018). Lattice paths and branched continued fractions: An infinite sequence of generalizations of the Stieltjes–Rogers
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C. Radoux (1992). Déterminants de Hankel et théorème de Sylvester, 28th SLC, Séminaire Lotharingien de Combinatoire, B28b, 9pp.
J. Riordan (1968). Combinatoiral identities, Wiley, New-York, 
J. Riordan (1975). The distribution of crossings of chords joining pairs of 2n points on a circle. Math. Comput., 29 (129), pp. 215–222. 

E. Roblet, J.M. Fedou and X.G. Viennot (1997). An identity on Thron’s dual continued fraction, Ann. Sci. Math. Québec, 21,  67-82.
E. Roblet and X.G.Viennot (1996). Théorie combinatoire des T-fractions et approximants de Padé en deux points, in Proc. 5th FPSAC
(Formal Power Series and Algebraic Combinatorics) , eds. A. Barlotti, M. Delest and R. Pinzani, Florence, Juin 1993, p. 401-414 et Discrete Maths., 153, 271-288.
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A. Sokal (2018). The Euler and Springer number as moment sequences, arXiv: 1804.04498 [math.C0].
A. Sokal and J.Zeng (2019), Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions,
in preparation, talk given by J. Zeng at the 81th SLC (Séminaire Lotharingien de Combinatoire), KrattenthalerFest, Strobl, Austria, Sept. 2018
R. Simion and D. Stanton (1994). Specializations of generalized Laguerre polynomials, SIAM J. Math. Anal. 25, 712-719.
R. Simion and D. Stanton (1996). Octabasic Laguerre polynomials and permutation statistics. J. Comp. Appl. Math. 68 , 297–329. 

H. S. Shin and J. Zeng (2012). The symmetric and unimodal expansion of Eulerian polynomials via continued fractions. European J. Combin. 33 , no. 2, 111–127. 

H. S. Shin and J. Zeng (2016). Symmetric unimodal expansions of excedances in colored permutations. European J. Combin. 52, part A, 174–196.
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V. Strehl (2017). Lacunary Laguerre Series from a Combinatorial Perspective. Sém. Lothar. Combin., B76c , 39 pp. 

R. A. Sulanke and G. Xin (2008). Hankel determinants for some common lattice paths. Adv. Appl. Math., 40:149-167.
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M. Vauchaussade de Chaumont and X.G. Viennot (1983). Problèmes orthogonaux et problèmes d’énumération en biologie moléculaire, SLC,
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X.G. Viennot (1982-83). Interprétations combinatoires des nombres d’Euler et de Genocchi,  (pdf, 9 Mo)
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X.G. Viennot (1985). A combinatorial theory for general orthogonal polynomials with extensions and applications, in: Pôlynomes Orthogonaux et Applications,

Bar-le-Duc 1984, C. Brezinski et al. (eds.), Lecture Notes in Mathematics, vol. 1171, Springer–Verlag.
X.G. Viennot (2000). A combinatorial interpratation of the quotient-difference algorithm, Proc. 12th FPSAC (Formal Power Series and Algebraic Combinatorics),
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[preliminary version as technical report LaBRI I-8611, Université de Bordeaux I, 1986; summary in annexe B of E. Roblet (1994)]
X.G. Viennot (2013)  Introduction to Chapter 3 on continued fraction, A survey of the 18 papers of P. Flajolet on continued fractions,
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J. Zeng (1988). Un calcul combinatoire des coefficients de linéarisation des produits de polynomes orthogonaux , C.R. Acad. Sc. Paris, t. 306, Séerie 1, 147-150. 
J. Zeng (1989). Linéarisation de produits de polynômes de Meixner, Krawtchouk et Charlier, S.I.A.M, J. Math. Anal., t. 21, 1349-1368. 
J. Zeng (1990). Calcul saalschützien des partitions et des dérangements colorés. SIAM J. Discrete Math. 3, no. 1, 149–156. 

J. Zeng (1990). Linéarisation de produits de polynômes de Meixner, Krawtchouk, et Charlier. SIAM J. Math. Anal. 21 , no. 5, 1349–1368. 

J. Zeng (1991). Counting a pair of permutations and the linearization coefficients for Jacobi polynomials, Actes de l'Atelier de Combinatoire franco-québecois,
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J. Zeng (1991). The β-extension of the multivariable Lagrange inversion formula. Stud. Appl. Math. 84, no. 2, 167–182. 

J. Zeng (1992). Weighted derangements and the linearization coefficients of orthogonal Sheffer polynomials. Proc. London Math. Soc. (3)65, no. 1, 1–22.
J. Zeng (1993). Enumérations de permutations et J-fractions continues. European J. Combin. 14 , no. 4, 373–382. 

J. Zeng (1995). The q-Stirling numbers, continued fractions and the q-Charlier and q-Laguerre polynomials, J. of Computational and applied Math., t.57, 413-424. 
J. Zeng (2000). On the powers of Motzkin paths , N. 44, Séminaire Lotharingien de Combinatoire,
J. Zeng (2018).  Some multivariate master polynomials for permutations, set partitions, and perfect matchings, and their continued fractions,
talk at SLC'81, (Séminaire Lotharingien de Combinatoire), Strobl, Austria, Sept 2018,  joint work with A. Sokal, 
KrattenthalerFest, dedicated to the 60th birthday of C. Krattenthaler