@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},
pages = {361--388},
year = {1988},
publisher = {EDP Sciences},
volume = {22},
number = {3},
mrnumber = {963597},
zbl = {0669.05002},
language = {fr},
url = {https://www.numdam.org/item/ITA_1988__22_3_361_0/}
}
TY - JOUR AU - Gouyou-Beauchamps, Dominique AU - Vauquelin, Bernard TI - Deux propriétés combinatoires des nombres de Schröder JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 1988 SP - 361 EP - 388 VL - 22 IS - 3 PB - EDP Sciences UR - https://www.numdam.org/item/ITA_1988__22_3_361_0/ LA - fr ID - ITA_1988__22_3_361_0 ER -
%0 Journal Article %A Gouyou-Beauchamps, Dominique %A Vauquelin, Bernard %T Deux propriétés combinatoires des nombres de Schröder %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 1988 %P 361-388 %V 22 %N 3 %I EDP Sciences %U https://www.numdam.org/item/ITA_1988__22_3_361_0/ %G fr %F 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. https://www.numdam.org/item/ITA_1988__22_3_361_0/
1. , 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. | Zbl | MR
2. , Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. | Zbl | MR
3. , Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. | Zbl | MR
4. , Restricted Plane Tree Representations of Four Motzkin-Catalan Equations, J.C.T., Ser. B, 22, 1977, p. 114-121. | Zbl | MR
5. , Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. | Zbl | MR
6. et , Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. | Zbl | MR
7. , A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. | Zbl | MR
8. , Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. | Zbl | MR
9. , A. Non Commutative Generalization of q-Analog of the Lagrange Inversion Formula, Trans. Amer. Math. Soc., vol. 257, 1980, p. 455-481. | Zbl | MR
10. et , Binomials Determinants, Paths and Hook Length Formulae, Advance in Maths., vol. 58, 1985, p. 300-321. | Zbl | MR
11. , Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. | Zbl | MR
12. , Deux propriétés combinatoires du langage de Lukasiewicz, R.A.I.R.O, vol. 3, 1975, p. 13-24. | Zbl | MR | Numdam
13. , 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. | Zbl | MR
14. et , Equivalence of the Two-Dimensional Directed Animal Problem to a One-Dimensional Path Problem, in Adv. in Appl. Math. (à paraître). | Zbl | MR
15. et , Continued Fractions, Analytic Theory and Applications, Encyclopedia of Math. and its Appl., vol. 11, G. C. ROTA éd., Addison-Wesley, Reading, 1980. | Zbl | MR
16. , Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. | Zbl | MR
17. , Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. | Zbl | MR
18. , The art of Computer Programming, vol. 1, Fundamental Algorithms, 2nd ed., Addison Wesley, Reading, Ma., 1973, p. 235-239 et 533-534. | MR
19. , Sur les éventails de segments, Cahiers du B.U.R.O., vol. 15, 1970, p. 3-41.
20. , Sur les partitions non croisées d'un cycle, Discrete Mathematics, vol. 1, n° 4, 1972, p. 333-350. | Zbl | MR
21. , Sur les hiérarchies de segments, Cahiers du B.U.R.O., vol. 20, 1973, p. 3-61.
22. , Aires des chemins surdiagonaux à étapes obliques permises, Cahiers du B.U.R.O., vol. 24, 1976, p. 9-18.
23. et , Lattice Paths with Diagonal Steps, Scripta math., vol. 26, 1963, p. 223-229. | Zbl | MR
24. , 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. | Zbl | MR
25. , On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. | Zbl | MR
26. , Combinatorial Identities, Wiley, New York, 1968, p. 148 | Zbl | MR
27. , Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. | Zbl | MR
28. , The Distribution of Crossing of Chords Joining Pairs of 2n Points on a Circle, Math. Comput., vol. 29, 1975, p. 215-222. | Zbl | MR
29. , A Schröder Triangle: Three Combinatorial Problems, Comb. Math. V: Proc. Fifth Aust. Conf., Lecture Notes in Math., 622, Springer-Verlag, Berlin, 1977. | Zbl | MR
30. , The Enumeration of a Family of Ladder Graphs Part I: Connective Relations, Quart. J. Math. Oxford, (2), 28, 1977, p. 421-431. | Zbl | MR
30. , The Enumeration of a Family of Ladder Graphs Part II: Schröder and Superconnective Relations, Quart. J. Math. Oxford, (2),31, 1980, p. 491-506. | Zbl | MR
32. , Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. | Zbl | MR
33. et , 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. et , 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. | Zbl | MR
35. , A Short Proof of an Identity of Touchard's Concerning Catalan Numbers, J.C.T., Ser. A, 20, 1976, p. 375-376. | Zbl | MR
36. , A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. | Zbl | MR
37. , Vier Kombinatorische Probleme, Z. fur M. Phys., 15, 1870, p. 361-376.
38. , A Handbook of Integer Sequences, Academic Press, New York, 1973. | Zbl | MR
39. et , Note on a "Square" Functional Equation, S.I.A.M. Review, vol. 12, n° 2, 1970, p. 277-279. | Zbl | MR
40. , Sur certaines équations fonctionnelles, in Proc. Inter. Congr. Mat., p. 465-472, Univ. of Toronto Press, Toronto, 1928. | JFM
41. et , Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Proc. Séminaire Lotharingien, Sainte-Croix-aux-Mines, mai 1983. | Zbl
42. et , 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. , Une théorie combinatoire des polynômes orthogonaux généraux, 217 p., Astérisque, Soc. Math. France (à paraître).
44. , Une théorie combinatoire des approximants de Padé, Réunion d'été de la Soc. Math, du Can., Québec, juin 1985, rapport Bordeaux, n° 8611.
45. , 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. | Zbl | MR | Numdam
