Deux propriétés combinatoires des nombres de Schröder
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 22 (1988) no. 3, p. 361-388
@article{ITA_1988__22_3_361_0,
     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},
     publisher = {EDP-Sciences},
     volume = {22},
     number = {3},
     year = {1988},
     pages = {361-388},
     zbl = {0669.05002},
     mrnumber = {963597},
     language = {fr},
     url = {http://www.numdam.org/item/ITA_1988__22_3_361_0}
}
Gouyou-Beauchamps, Dominique; Vauquelin, Bernard. Deux propriétés combinatoires des nombres de Schröder. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 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 329910 | Zbl 0299.05002

2. W. G. Brown, Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. | MR 1533479 | Zbl 0136.21204

3. L. Comtet, Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. | MR 460128 | Zbl 0283.05001

4. R. Donaghey, Restricted Plane Tree Representations of Four Motzkin-Catalan Equations, J.C.T., Ser. B, 22, 1977, p. 114-121. | MR 432532 | Zbl 0352.05028

5. R. Donaghey, Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. | MR 584162 | Zbl 0463.05038

6. R. Donaghey et L. W. Shapiro, Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. | MR 505544 | Zbl 0417.05007

7. W. J. R. Eplett, A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. | MR 534947 | Zbl 0393.05014

8. P. Flajolet, Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. | MR 592851 | Zbl 0445.05014

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 552269 | Zbl 0459.05014

10. I. M. Gessel et G. Viennot, Binomials Determinants, Paths and Hook Length Formulae, Advance in Maths., vol. 58, 1985, p. 300-321. | MR 815360 | Zbl 0579.05004

11. H. W. Gould, Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. | MR 401633 | Zbl 0327.10001

12. D. Gouyou-Beauchamps, Deux propriétés combinatoires du langage de Lukasiewicz, R.A.I.R.O, vol. 3, 1975, p. 13-24. | Numdam | MR 395351 | Zbl 0337.05010

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 927762 | Zbl 0611.05003

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 956559 | Zbl 0727.05036

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 595864 | Zbl 0603.30009

16. C. Jordan, Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. | MR 183987 | Zbl 0154.33901

17. D. A. Klarner, Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. | MR 292690 | Zbl 0205.54702

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 378456

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 309747 | Zbl 0231.05014

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 150064 | Zbl 0111.24105

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 24411 | Zbl 0032.24607

25. G. Polya, On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. | MR 236031 | Zbl 0327.05010

26. J. Riordan, Combinatorial Identities, Wiley, New York, 1968, p. 148 | MR 231725 | Zbl 0194.00502

27. J. Riordan, Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. | MR 409241 | Zbl 0308.05115

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 366686 | Zbl 0319.05004

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 462964 | Zbl 0368.05004

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 491365 | Zbl 0373.05045

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 596981 | Zbl 0451.05034

32. D. G. Rogers, Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. | MR 522725 | Zbl 0398.05007

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 526754

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 641254 | Zbl 0469.05005

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 406819 | Zbl 0337.05012

36. L. W. Shapiro, A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. | MR 387069 | Zbl 0323.05004

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 357292 | Zbl 0286.10001

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 260602 | Zbl 0206.29301

40. J. Touchard, Sur certaines équations fonctionnelles, in Proc. Inter. Congr. Mat., p. 465-472, Univ. of Toronto Press, Toronto, 1928. | JFM 54.0440.03

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 0977.33500

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 0579.92012

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 768962 | Zbl 0563.60095