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

How to cite

top

Gouyou-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. 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. 2. W. G. BROWN, Historical Note on a Recurrent Combinatorial Problem, Amer. Math. Monthly, vol.72, 1965, p. 973-977. Zbl0136.21204MR1533479
  3. 3. L. COMTET, Advanced Combinatorics, D. Reidel publ. comp., Boston, 1974, p. 56. Zbl0283.05001MR460128
  4. 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. 5. R. DONAGHEY, Automorphisms on Catalan Trees and Bracketings, J.C.T., Ser. B, 29, 1980, p. 75-90. Zbl0463.05038MR584162
  6. 6. R. DONAGHEY et L. W. SHAPIRO, Motzkin Numbers, J.C.T., Ser. A, 23, 1977, p. 291-301. Zbl0417.05007MR505544
  7. 7. W. J. R. EPLETT, A Note About the Catalan Triangle, Discrete Math., vol. 25, 1979, p. 289-291. Zbl0393.05014MR534947
  8. 8. P. FLAJOLET, Combinatorial Aspects of Continued Fractions, Discrete Math., vol. 32, 1980, p. 125-161. Zbl0445.05014MR592851
  9. 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. 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. 11. H. W. GOULD, Research Bibliography of Two Special Number Sequences, rev. ed., Combinatorial Research Institute, Morgantown, W. Va., 1977. Zbl0327.10001MR401633
  12. 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. 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. 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. 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. 16. C. JORDAN, Calculus of Finites Differences, Chelsea Publishing Company, New York, 1950, p. 449. Zbl0154.33901MR183987
  17. 17. D. A. KLARNER, Correspondance Between Plane Trees and Binary Sequences, J.C.T., vol. 9, 1970, p. 401-411. Zbl0205.54702MR292690
  18. 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. 19. G. KREWERAS, Sur les éventails de segments, Cahiers du B.U.R.O., vol. 15, 1970, p. 3-41. 
  20. 20. G. KREWERAS, Sur les partitions non croisées d'un cycle, Discrete Mathematics, vol. 1, n° 4, 1972, p. 333-350. Zbl0231.05014MR309747
  21. 21. G. KREWERAS, Sur les hiérarchies de segments, Cahiers du B.U.R.O., vol. 20, 1973, p. 3-61. 
  22. 22. G. KREWERAS, Aires des chemins surdiagonaux à étapes obliques permises, Cahiers du B.U.R.O., vol. 24, 1976, p. 9-18. 
  23. 23. L. MOSER et W. ZAYACHKOWSKI, Lattice Paths with Diagonal Steps, Scripta math., vol. 26, 1963, p. 223-229. Zbl0111.24105MR150064
  24. 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. 25. G. POLYA, On the Number of Certain Lattice Polygons, J. Comb. Theory, vol. 6, 1969, p. 102-105. Zbl0327.05010MR236031
  26. 26. J. RIORDAN, Combinatorial Identities, Wiley, New York, 1968, p. 148 Zbl0194.00502MR231725
  27. 27. J. RIORDAN, Enumeration of Plane Trees by Branchs and Endpoints, J.C.T., Ser. A, 19, 1975, p. 214-222. Zbl0308.05115MR409241
  28. 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. 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. 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
  31. 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. 32. D. G. ROGERS, Pascal Triangles, Catalan Numbers and Renewal Arrays, Discrete Math., vol. 22, 1978, p. 301-310. Zbl0398.05007MR522725
  33. 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. 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. 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. 36. L. W. SHAPIRO, A Catalan Triangle, Discrete Math., vol. 14, 1976, p. 83-90. Zbl0323.05004MR387069
  37. 37. SCHRÖDER, Vier Kombinatorische Probleme, Z. fur M. Phys., 15, 1870, p. 361-376. 
  38. 38. N. J. A. SLOANE, A Handbook of Integer Sequences, Academic Press, New York, 1973. Zbl0286.10001MR357292
  39. 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. 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. 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. 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. 43. G. VIENNOT, Une théorie combinatoire des polynômes orthogonaux généraux, 217 p., Astérisque, Soc. Math. France (à paraître). 
  44. 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. 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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.