Skip to main content
SpringerLink
Log in

A combinatorial theory for general orthogonal polynomials with extensions and applications

  • II. Conferenciers Ou Contributeurs
  • Conference paper
  • First Online:
Polynômes Orthogonaux et Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1171))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G. E. ANDREWS, The Rogers-Ramanujan reciprocal and Minc's partition function, Pacific J. Math., 95 (1981), 251–256.

    Article  MathSciNet  MATH  Google Scholar 

  2. R. BAXTER, Exactly solved models in statistical mechanics, Academic Press, New York, 1982.

    MATH  Google Scholar 

  3. F. BERGERON, Une approche combinatoire de la méthode de Weisner, in this volume.

    Google Scholar 

  4. P. CARTIER, D. FOATA, Problèmes combinatoires de commutation et réarrangements, Lecture Notes in Maths, no 85, Springer Verlag, New York/Berlin, 1969.

    MATH  Google Scholar 

  5. T. S. CHIHARA, An introduction to orthogonal polynomials, Gordon an Breach, New York/London/Paris, 1978.

    MATH  Google Scholar 

  6. M. DESAINTE-CATHERINE, G. VIENNOT, Combinatorial interpretation of integrals of products of Hermite, Laguerre and Tchebycheff polynomials, in this volume.

    Google Scholar 

  7. D. DHAR, Equivalence of the two-dimensional directed-site animal problem to Baxter's hard-square lattice-gas model, Phys. Rev. Lett., 49 (1982), 959–962.

    Article  MathSciNet  Google Scholar 

  8. A. DRAUX, Polynômes orthogonaux formels, applications, Lecture Notes in Maths, no 974, Springer-Verlag, New York/Berlin, 1983.

    Book  MATH  Google Scholar 

  9. S. DULUCQ, G. VIENNOT, The Cartier-Foata commutation monoid revisited with heaps of pieces, in preparation.

    Google Scholar 

  10. P. FLAJOLET, Combinatorial aspects of continued fractions, Discrete Maths., 32 (1980), 125–161.

    Article  MathSciNet  MATH  Google Scholar 

  11. P. FLAJOLET, J. FRANÇON, J. VUILLEMIN, Sequence of operations analysis for dynamic data structures, J. of Algorithms, 1 (1980), 111–141.

    Article  MathSciNet  MATH  Google Scholar 

  12. D. FOATA, La série génératrice exponentielle dans les problèmes d'énumération, Presses de l'Univ. de Montréal, Montréal, 1974.

    MATH  Google Scholar 

  13. D. FOATA, Combinatoire des identités sur les polynômes orthogonaux, Proc. du Congrès International des Mathématiciens, section 16, Combinatoric and Mathematical Programming, Warsaw, 1983.

    Google Scholar 

  14. J. FRANÇON, Histoires de fichiers, RAIRO Info. Théor., 12 (1978), 49–67.

    MathSciNet  MATH  Google Scholar 

  15. J. FRANÇON, G. VIENNOT, Permutations selon les pics, creux, doubles montées, doubles descentes, nombres d'Euler et nombres de Genocchi, Discrete Math., 28 (1979), 21–35.

    Article  MathSciNet  MATH  Google Scholar 

  16. A. GARSIA, A q-analogue of the Lagrange inversion formula, Houston J. Math., 7 (1981), 205–237.

    MathSciNet  MATH  Google Scholar 

  17. I. GESSEL, A non commutative generalization and q-analog of the Lagrange inversion formula, Trans. Amer. Math. Soc., 257 (1980), 455–481.

    MathSciNet  MATH  Google Scholar 

  18. I. GESSEL, G. VIENNOT, Combinatorial interpretation of determinants with weighted paths, in preparation; Binomial determinant, paths and hook lengths formulae, to appear in Adv. in Maths.

    Google Scholar 

  19. C. D. GODSIL, Matchings and walks in graphs, J. Graph Th., 5 (1981), 285–291.

    Article  MathSciNet  MATH  Google Scholar 

  20. C. D. GODSIL, Real graph polynomials, Proc. Conf. Waterloo, 1982.

    Google Scholar 

  21. I. GOULDEN, D. JACKSON, Combinatorial enumeration, John Wiley and sons, New York, 1983.

    MATH  Google Scholar 

  22. D. GOUYOU-BEAUCHAMPS, G. VIENNOT, The number of directed animals, preprint.

    Google Scholar 

  23. V. HAKIM, J.-P. NADAL, Exact results for 2d directed animals on a strip of finite width, J. Phys. A: Math. Gen., 16 (1983), L 213–L 218.

    Article  MathSciNet  Google Scholar 

  24. J. HEILMAN, E. H. LIEB, Theory of monominer-dimer systems, Comm. Math. Phys., 25 (1972), 190–232.

    Article  MathSciNet  Google Scholar 

  25. W. B. JONES, W. J. THRON, Continued fractions, Analytic Theory and Applications, Encycl. of Math. and its Appl., vol. 11, G. C. Rota ed., Addison-Wesley, Reading, 1980.

    Google Scholar 

  26. A. JOYAL, Une théorie combinatoire des séries formelles, Adv. in Math., 42 (1981), 1–82.

    Article  MathSciNet  MATH  Google Scholar 

  27. J.-P. NADAL, B. DERRIDA, J. VANNIMENUS, Directed lattice animals in two dimensions: numerical and exact results, J. Physique, 43 (1982), 1561.

    Article  MathSciNet  Google Scholar 

  28. G. C. ROTA, D. KAHANER, A. ODLYZKO, Finite operator calculus, J. Math. Anal. Appl., 42 (1973), 685–760.

    Article  MathSciNet  MATH  Google Scholar 

  29. V. J. SKOROBOGAT'KO, N. S. DRONJUK, O. I. BOBIK, B. I. PTASNIK, Branching continued fractions (in ukrainian), Dopovidi Akad. Nauk. Ukrain. RSR, Ser. A (1967), 131–134.

    Google Scholar 

  30. W. SIEMASZKO, On some conditions for convergence of branched continued fractions, in "Padé Approximation and its applications", Proc. Amsterdam 1980, De Bruin and van Rossum ed., Lecture Notes in Math. no 888, Springer Verlag, New York/Berlin, 1981, 363–370.

    Google Scholar 

  31. V. STREHL, Quelques constructions combinatoires reliées aux polynômes orthogonaux classiques, in this volume.

    Google Scholar 

  32. I. TINOCO, O. C. UHLENBECK, M. D. LEVINE, Estimation of secondary structure in rilonucleic acids, Nature 230 (1971), 362–367.

    Article  Google Scholar 

  33. M. VAUCHAUSSADE de CHAUMONT, G. VIENNOT, Enumeration of RNAs secondary structures by complexity, in preparation. Abstract in "Internat. Conf. on Maths. in Biology and Medicine", Bari, Italy, 1983.

    Google Scholar 

  34. G. VIENNOT, Une théorie combinatoire des polynômes orthogonaux généraux, Notes de conférence, Univ. du Québec à Montréal, Montréal, 1984, 217 pages.

    Google Scholar 

  35. G. VIENNOT, Problèmes combinatoires posés par la physique statistique, Séminaire Bourbaki, 36ème année, 1983/84, no 626, in "Astérisque" no 121–122 (1985), 225–246, Soc. Math. France.

    Google Scholar 

  36. G. VIENNOT, Combinatorial solution of the 2D directed lattice animals problem with heaps of dimers, in preparation.

    Google Scholar 

  37. G. VIENNOT, Directed animals and combinatorial interpretation of the density of a gaz, in preparation.

    Google Scholar 

  38. G. VIENNOT, Empilements: théorie et applications, in Proc. Congrès "Combinatoire énumérative" UQAM, Montréal, 1985.

    Google Scholar 

  39. M. S. WATERMAN, Secondary structure of single-stranted nucleic acids, in "Studies in Foundations and Combinatoris", Adv. in Maths. Suppl. Studies, 1 (1978), 167–212.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. U. E. R. de Mathématiques et Informatique Université de Bordeaux I, 33405, Talence, France

    Gérard Viennot

Authors
  1. Gérard Viennot
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Claude Brezinski André Draux Alphonse P. Magnus Pascal Maroni André Ronveaux

Rights and permissions

Reprints and permissions

Copyright information

© 1985 Springer-Verlag

About this paper

Cite this paper

Viennot, G. (1985). A combinatorial theory for general orthogonal polynomials with extensions and applications. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076539

Download citation

  • DOI: https://doi.org/10.1007/BFb0076539

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation