@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}, 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/} }
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 - http://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 http://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. http://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. | MR | Zbl
,2. Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. | MR | Zbl
,3. Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. | MR | Zbl
,4. Restricted Plane Tree Representations of Four Motzkin-Catalan Equations, J.C.T., Ser. B, 22, 1977, p. 114-121. | MR | Zbl
,5. Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. | MR | Zbl
,6. Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. | MR | Zbl
et ,7. A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. | MR | Zbl
,8. Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. | MR | Zbl
,9. 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. Binomials Determinants, Paths and Hook Length Formulae, Advance in Maths., vol. 58, 1985, p. 300-321. | MR | Zbl
et ,11. Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. | MR | Zbl
,12. Deux propriétés combinatoires du langage de Lukasiewicz, R.A.I.R.O, vol. 3, 1975, p. 13-24. | Numdam | MR | Zbl
,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. | MR | Zbl
,14. Equivalence of the Two-Dimensional Directed Animal Problem to a One-Dimensional Path Problem, in Adv. in Appl. Math. (à paraître). | MR | Zbl
et ,15. Continued Fractions, Analytic Theory and Applications, Encyclopedia of Math. and its Appl., vol. 11, G. C. ROTA éd., Addison-Wesley, Reading, 1980. | MR | Zbl
et ,16. Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. | MR | Zbl
,17. Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. | MR | Zbl
,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. | MR | Zbl
,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. Lattice Paths with Diagonal Steps, Scripta math., vol. 26, 1963, p. 223-229. | MR | Zbl
et ,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. | MR | Zbl
,25. On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. | MR | Zbl
,26. Combinatorial Identities, Wiley, New York, 1968, p. 148 | MR | Zbl
,27. Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. | MR | Zbl
,28. 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. 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. 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. 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. Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. | MR | Zbl
,33. 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
et ,34. 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
et ,35. 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. A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. | MR | Zbl
,37. Vier Kombinatorische Probleme, Z. fur M. Phys., 15, 1870, p. 361-376.
,38. A Handbook of Integer Sequences, Academic Press, New York, 1973. | MR | Zbl
,39. Note on a "Square" Functional Equation, S.I.A.M. Review, vol. 12, n° 2, 1970, p. 277-279. | MR | Zbl
et ,40. Sur certaines équations fonctionnelles, in Proc. Inter. Congr. Mat., p. 465-472, Univ. of Toronto Press, Toronto, 1928. | JFM
,41. Polynômes orthogonaux et problèmes d'énumération en biologie moléculaire, Proc. Séminaire Lotharingien, Sainte-Croix-aux-Mines, mai 1983. | Zbl
et ,42. 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
et ,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. | Numdam | MR | Zbl
,