Deux propriétés combinatoires des nombres de Schröder
Dominique Gouyou-Beauchamps; Bernard Vauquelin
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1988)
- Volume: 22, Issue: 3, page 361-388
- ISSN: 0988-3754
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topGouyou-Beauchamps, Dominique, and Vauquelin, Bernard. "Deux propriétés combinatoires des nombres de Schröder." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 22.3 (1988): 361-388. <http://eudml.org/doc/92313>.
@article{Gouyou1988,
author = {Gouyou-Beauchamps, Dominique, Vauquelin, Bernard},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {Schröder number; Catalan number; coloured lattice paths},
language = {fre},
number = {3},
pages = {361-388},
publisher = {EDP-Sciences},
title = {Deux propriétés combinatoires des nombres de Schröder},
url = {http://eudml.org/doc/92313},
volume = {22},
year = {1988},
}
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
PB - EDP-Sciences
VL - 22
IS - 3
SP - 361
EP - 388
LA - fre
KW - Schröder number; Catalan number; coloured lattice paths
UR - http://eudml.org/doc/92313
ER -
References
top- 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. Zbl0299.05002MR329910
- 2. W. G. BROWN, Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. Zbl0136.21204MR1533479
- 3. L. COMTET, Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. Zbl0283.05001MR460128
- 4. R. DONAGHEY, Restricted Plane Tree Representations of Four Motzkin-Catalan Equations, J.C.T., Ser. B, 22, 1977, p. 114-121. Zbl0352.05028MR432532
- 5. R. DONAGHEY, Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. Zbl0463.05038MR584162
- 6. R. DONAGHEY et L. W. SHAPIRO, Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. Zbl0417.05007MR505544
- 7. W. J. R. EPLETT, A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. Zbl0393.05014MR534947
- 8. P. FLAJOLET, Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. Zbl0445.05014MR592851
- 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. Zbl0459.05014MR552269
- 10. I. M. GESSEL et G. VIENNOT, Binomials Determinants, Paths and Hook Length Formulae, Advance in Maths., vol. 58, 1985, p. 300-321. Zbl0579.05004MR815360
- 11. H. W. GOULD, Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. Zbl0327.10001MR401633
- 12. D. GOUYOU-BEAUCHAMPS, Deux propriétés combinatoires du langage de Lukasiewicz, R.A.I.R.O, vol. 3, 1975, p. 13-24. Zbl0337.05010MR395351
- 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. Zbl0611.05003MR927762
- 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). Zbl0727.05036MR956559
- 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. Zbl0603.30009MR595864
- 16. C. JORDAN, Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. Zbl0154.33901MR183987
- 17. D. A. KLARNER, Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. Zbl0205.54702MR292690
- 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. MR378456
- 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. Zbl0231.05014MR309747
- 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. Zbl0111.24105MR150064
- 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. Zbl0032.24607MR24411
- 25. G. POLYA, On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. Zbl0327.05010MR236031
- 26. J. RIORDAN, Combinatorial Identities, Wiley, New York, 1968, p. 148 Zbl0194.00502MR231725
- 27. J. RIORDAN, Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. Zbl0308.05115MR409241
- 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. Zbl0319.05004MR366686
- 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. Zbl0368.05004MR462964
- 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. Zbl0373.05045MR491365
- 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. Zbl0451.05034MR596981
- 32. D. G. ROGERS, Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. Zbl0398.05007MR522725
- 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. MR526754
- 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. Zbl0469.05005MR641254
- 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. Zbl0337.05012MR406819
- 36. L. W. SHAPIRO, A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. Zbl0323.05004MR387069
- 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. Zbl0286.10001MR357292
- 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. Zbl0206.29301MR260602
- 40. J. TOUCHARD, Sur certaines équations fonctionnelles, in Proc. Inter. Congr. Mat., p. 465-472, Univ. of Toronto Press, Toronto, 1928. Zbl54.0440.03JFM54.0440.03
- 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. Zbl0977.33500
- 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. Zbl0579.92012
- 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. Zbl0563.60095MR768962
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