Deux propriétés combinatoires des nombres de Schröder
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 22 (1988) no. 3, pp. 361-388.
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     author = {Gouyou-Beauchamps, Dominique and Vauquelin, Bernard},
     title = {Deux propri\'et\'es combinatoires des nombres de {Schr\"oder}},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {361--388},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {3},
     year = {1988},
     mrnumber = {963597},
     zbl = {0669.05002},
     language = {fr},
     url = {http://www.numdam.org/item/ITA_1988__22_3_361_0/}
}
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Gouyou-Beauchamps, Dominique; Vauquelin, Bernard. Deux propriétés combinatoires des nombres de Schröder. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 22 (1988) no. 3, pp. 361-388. http://www.numdam.org/item/ITA_1988__22_3_361_0/

1. R. Alter, Some Remarks and Results on Catalan Numbers, in Proceedings of the Second Louisiana Conference on Combinatorics, Graph Theory and Computing, Baton Rouge, 1971, p. 109-132. | MR | Zbl

2. W. G. Brown, Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. | MR | Zbl

3. L. Comtet, Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. | MR | Zbl

4. R. Donaghey, Restricted Plane Tree Representations of Four Motzkin-Catalan Equations, J.C.T., Ser. B, 22, 1977, p. 114-121. | MR | Zbl

5. R. Donaghey, Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. | MR | Zbl

6. R. Donaghey et L. W. Shapiro, Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. | MR | Zbl

7. W. J. R. Eplett, A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. | MR | Zbl

8. P. Flajolet, Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. | MR | Zbl

9. I. Gessel, A. Non Commutative Generalization of q-Analog of the Lagrange Inversion Formula, Trans. Amer. Math. Soc., vol. 257, 1980, p. 455-481. | MR | Zbl

10. I. M. Gessel et G. Viennot, Binomials Determinants, Paths and Hook Length Formulae, Advance in Maths., vol. 58, 1985, p. 300-321. | MR | Zbl

11. H. W. Gould, Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. | MR | Zbl

12. D. Gouyou-Beauchamps, Deux propriétés combinatoires du langage de Lukasiewicz, R.A.I.R.O, vol. 3, 1975, p. 13-24. | Numdam | MR | Zbl

13. D. Gouyou-Beauchamps, Chemins sous-diagonaux et tableaux de Young, in Combinatoire énumérative, p. 112-125, Lecture Notes in Math., n° 1234, G. LABELLE et P. LEROUX éd., Springer-Verlag, Berlin, 1986. | MR | Zbl

14. D. Gouyou-Beauchamps et G. Viennot, Equivalence of the Two-Dimensional Directed Animal Problem to a One-Dimensional Path Problem, in Adv. in Appl. Math. (à paraître). | MR | Zbl

15. W. B. Jones et W. J. Thron, Continued Fractions, Analytic Theory and Applications, Encyclopedia of Math. and its Appl., vol. 11, G. C. ROTA éd., Addison-Wesley, Reading, 1980. | MR | Zbl

16. C. Jordan, Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. | MR | Zbl

17. D. A. Klarner, Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. | MR | Zbl

18. D. E. Knuth, The art of Computer Programming, vol. 1, Fundamental Algorithms, 2nd ed., Addison Wesley, Reading, Ma., 1973, p. 235-239 et 533-534. | MR

19. G. Kreweras, Sur les éventails de segments, Cahiers du B.U.R.O., vol. 15, 1970, p. 3-41.

20. G. Kreweras, Sur les partitions non croisées d'un cycle, Discrete Mathematics, vol. 1, n° 4, 1972, p. 333-350. | MR | Zbl

21. G. Kreweras, Sur les hiérarchies de segments, Cahiers du B.U.R.O., vol. 20, 1973, p. 3-61.

22. G. Kreweras, Aires des chemins surdiagonaux à étapes obliques permises, Cahiers du B.U.R.O., vol. 24, 1976, p. 9-18.

23. L. Moser et W. Zayachkowski, Lattice Paths with Diagonal Steps, Scripta math., vol. 26, 1963, p. 223-229. | MR | Zbl

24. T. Motzkin, Relation Between Hypersurface Cross Ratio and a Combinatorial Formula for Partitions of a Polygon, for Permanent Preponderance and for Non-Associative Products, Bul. Amer. Math. Soc., vol. 54, 1948, p. 352-360. | MR | Zbl

25. G. Polya, On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. | MR | Zbl

26. J. Riordan, Combinatorial Identities, Wiley, New York, 1968, p. 148 | MR | Zbl

27. J. Riordan, Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. | MR | Zbl

28. J. Riordan, The Distribution of Crossing of Chords Joining Pairs of 2n Points on a Circle, Math. Comput., vol. 29, 1975, p. 215-222. | MR | Zbl

29. D. G. Rogers, A Schröder Triangle: Three Combinatorial Problems, Comb. Math. V: Proc. Fifth Aust. Conf., Lecture Notes in Math., 622, Springer-Verlag, Berlin, 1977. | MR | Zbl

30. D. G. Rogers, The Enumeration of a Family of Ladder Graphs Part I: Connective Relations, Quart. J. Math. Oxford, (2), 28, 1977, p. 421-431. | MR | Zbl

30. D. G. Rogers, The Enumeration of a Family of Ladder Graphs Part II: Schröder and Superconnective Relations, Quart. J. Math. Oxford, (2),31, 1980, p. 491-506. | MR | Zbl

32. D. G. Rogers, Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. | MR | Zbl

33. D. G. Rogers et L. W. Shapiro, Some Correspondance Involving the Schröder Numbers and Relations, in Comb. Math., Proc. of the Intern. Conf., Camberra, 1977, Lecture Notes in Math., vol. 686, Springer-Verlag, Berlin, 1978, p. 267-276. | MR

34. D. G. Rogers et L. W. Shapiro, Deques, Trees and Lattice Paths, in Comb. Math. VIII Proc., Geelong, Australia, 1980, Lecture Notes in Math., vol. 884, Springer-Verlag, Berlin, 1981, p. 293-303. | MR | Zbl

35. L. W. Shapiro, A Short Proof of an Identity of Touchard's Concerning Catalan Numbers, J.C.T., Ser. A, 20, 1976, p. 375-376. | MR | Zbl

36. L. W. Shapiro, A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. | MR | Zbl

37. Schröder, Vier Kombinatorische Probleme, Z. fur M. Phys., 15, 1870, p. 361-376.

38. N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, New York, 1973. | MR | Zbl

39. R. G. Stanton et D. D. Cowan, Note on a "Square" Functional Equation, S.I.A.M. Review, vol. 12, n° 2, 1970, p. 277-279. | MR | Zbl

40. J. Touchard, Sur certaines équations fonctionnelles, in Proc. Inter. Congr. Mat., p. 465-472, Univ. of Toronto Press, Toronto, 1928. | JFM

41. M. Vauchaussade De Chaumont et G. Viennot, Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Proc. Séminaire Lotharingien, Sainte-Croix-aux-Mines, mai 1983. | Zbl

42. M. Vauchaussade De Chaumont et G. Viennot, Enumeration of RNAs secondary structure by complexity, in Mathematics in Medecine and Biology, V. CAPASSO, E. GROSSO and S. L. PAVEN-FONTANA éd., Lecture Notes in Biomath., n° 57, Springer-Verlag, Berlin, 1985, p. 360-365. | Zbl

43. G. Viennot, Une théorie combinatoire des polynômes orthogonaux généraux, 217 p., Astérisque, Soc. Math. France (à paraître).

44. G. Viennot, Une théorie combinatoire des approximants de Padé, Réunion d'été de la Soc. Math, du Can., Québec, juin 1985, rapport Bordeaux, n° 8611.

45. G. Viennot, Problèmes combinatoires posés par la physique statistique, Séminaire Bourbaki, 36e année, 1983/1984. exposé n° 626, in Astérisque, Soc. Math. France, n° 121-122, 1985, p. 225-246. | Numdam | MR | Zbl