Skip to main content

Some new computational methods in the theory of species

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1234))

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

Buying options

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   59.95
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Barnabei, A. Brini and G. Nicoletti. A General Umbral Calculus in infinitely many Variables, Adv. in Mathematics, 50, 1983, 49–93.

    Article  MathSciNet  MATH  Google Scholar 

  2. H. Bass, E. H. Connel and D. Wright. The Jacobian conjecture: Reduction of degree and formal expansion of the inverse, Bull. Amer. Math. Soc. (N.S.) 7, 1982, 287–330.

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Barnabei. Lagrange Inversion in infinitely many Variables, J. of Mathematical Analysis and Applications, Vol. 108, No. 1, 1985, 198–210.

    Article  MathSciNet  MATH  Google Scholar 

  4. F. Bergeron. Une systématique de la combinatoire énumérative, Ph.D. Thesis, U. de Montréal-UQAM, 1986.

    Google Scholar 

  5. F. Bergeron. Modèles combinatoires de familles de polynômes or thogonaux, Rapp. Tech. no.3, Dép. Math. et Info., UQAM, 1984, (submitted for publication).

    Google Scholar 

  6. F. Bergeron. Une approoche combinatoire de la méthode de Weisner, in Polynômes orthogonaux et applications, Proc. Bar-le-Duc (1984), ed. C. Brézinski, A. Draux, A.P. Magnus, P. Maroni, A. Ronveaux, Springer Lecture Notes in Mathematics., no. 1171, 1985, 111–119.

    Google Scholar 

  7. F. Bergeron. Combinatorial Representations of some Lie Groups and Lie Algebras, (this volume).

    Google Scholar 

  8. N. G. de Bruijn. Enumerative combinatorial problems concerning structures. Nieuw Arch. Wisk. (3), 11, 1963, 142–161.

    MathSciNet  MATH  Google Scholar 

  9. N. G. de Bruijn. Enumeration of tree-shaped molecules. Recent Progress in Combinatorics, (Proc. 3rd Waterloo Conf. on Combinatorics, 1968), Academic, New York, 1969, 59–68.

    MATH  Google Scholar 

  10. N. G. de Bruijn and D.A. Klarner. Multisets of aperiodic cycles. SIAM J. Algebraic Discrete Methods, 3, 1982, 359–368.

    Article  MathSciNet  MATH  Google Scholar 

  11. R. P. Brent and H. T. Kung. O((n log n)3/2) algorithms for composition and reversion of power series in "Analytic Computational Complexity", Proceedings of the Symposium on Analytic Computational Complexity, Carnegie-Mellon Univ., Pittsburgh, Penn., 1975, Acad. Press, New York, 1976, 217–225.

    Chapter  Google Scholar 

  12. R. P. Brent and H. T. Kung. Fast algorithms for manipulating formal power series. J. Assoc. Comput. Mach. 25, 1978, 581–595.

    Article  MathSciNet  MATH  Google Scholar 

  13. C. C. Cadogan. The Möbius function and connected graphs, J. Comb. Theory, Ser. B, 11, 1971, 193–200.

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Comtet. Analyse combinatoire, (2 volumes), Collection SUP, Presses Universitaires de France, 1970.

    Google Scholar 

  15. H. Décoste. Séries indicatrices d'espèces pondérées et g-analogues. Ph.D. Thesis, U. de Montréal-UQAM, (under preparation).

    Google Scholar 

  16. H. Décoste, G. Labelle et P. Leroux. Une approche combinatoire pour l'itération de Newton-Raphson, Adv. in Applied Math. 3, 1982, 407–416.

    Article  MATH  Google Scholar 

  17. D. Foata (U. de Strasbourg) et J. Labelle. Modèles combinatoires pour les polynômes de Meixner, J. Européen de Combinatoire, 1983, 305–311.

    Google Scholar 

  18. D. Foata (U. de Strasbourg) et P. Leroux. Polynômes de Jacobi, interprétation combinatoire et fonction génératrice, Proc. Amer. Math. Soc. 87, 1983, 47–53.

    MathSciNet  MATH  Google Scholar 

  19. I. Gessel. A Combinatorial Proof of the Multivariable Lagrange Inversion Formula, (manuscript).

    Google Scholar 

  20. I. J. Good. Generalization to several variables of Lagrange's expansion with applications to stochastic processes, Proc. Cambridge Phil. Soc. 56, 1960, 367–380.

    Article  MathSciNet  MATH  Google Scholar 

  21. P. Hanlon. A Cycle Index Sum Inversion Theorem, J. Comb. Theory, Series A, 30, 1981, 248–269.

    Article  MathSciNet  MATH  Google Scholar 

  22. P. Hanlon. The Characters of the Wreath Product Group Acting on the Homology Groups of the Dowling Lattices, J. of Algebra 91, No.2, 1984, 430–463.

    Article  MathSciNet  MATH  Google Scholar 

  23. F. Harary, E. M. Palmer. Graphical Enumeration, Acad. Press, N.Y., 1973.

    MATH  Google Scholar 

  24. P. Hanlon and R. W. Robinson, Counting Bridgeless Graphs, J. Comb. Theory, Series B, 33, 1982, 276–305.

    Article  MathSciNet  MATH  Google Scholar 

  25. G. H. Hardy, E. M. Wright. An Introduction to the Theory of Numbers 4th ed., Oxford: Clarendon Press, 1960.

    MATH  Google Scholar 

  26. S. A. Joni. Lagrange inversion in higher dimensions and umbral operators, Linear and Multilinear Algebra 6, 1978, 111–121.

    Article  MathSciNet  MATH  Google Scholar 

  27. A. Joyal. Une théorie combinatoire des séries formelles, Adv. in Math. 42, 1981, 1–82.

    Article  MathSciNet  MATH  Google Scholar 

  28. A. Joyal. Règle des signes en algèbre combinatoire, C.R. Math. Rep. Acad. Sci. Canada, VII, 5, 1985, 285–290.

    MathSciNet  MATH  Google Scholar 

  29. A. Joyal, Calcul intégral combinatoire et homologie des groupes symétriques, C.R. Math. Rep. Acad. Sci. Canada, VII, 6, 1985, 337–342.

    MathSciNet  MATH  Google Scholar 

  30. A. Joyal. Foncteurs analytiques et espèces de structures, (this volume).

    Google Scholar 

  31. G. James and A. Kerber. The Representation Theory of the Symmetric Group, Encycl. of Maths, Vol. 16, Addison-Wesley, N.Y., 1981.

    Google Scholar 

  32. G. Labelle. Une nouvelle démonstration combinatoire des formules d'inversion de Lagrange, Adv. in Math. 42, 1981, 217–247.

    Article  MathSciNet  MATH  Google Scholar 

  33. G. Labelle. Éclosions combinatoires appliquées à l'inversion multidimensionnelle des séries formelles, J. of Comb. Theory Ser. A, 39, No. 1, 1985, 52–82.

    Article  MathSciNet  MATH  Google Scholar 

  34. G. Labelle. Une combinatoire sous-jacente au théorème des fonctions implicites, J. of Combinatorial Theory, Ser. A, 40, No.2, 1985, 377–393.

    Article  MathSciNet  MATH  Google Scholar 

  35. G. Labelle. On Combinatorial Differential Equations, J. of Math. Anal. and Appl., 113, No.2, Feb. 1986, 344–381.

    Article  MathSciNet  MATH  Google Scholar 

  36. G. Labelle. The computation of the cycle index series of some combinatorial species, Lecture notes, Combinatorial Year, M.I.T., Nov. 1984.

    Google Scholar 

  37. G. Labelle. The Cyclic Type of Combinatorial Species, Lecture notes, Special Session on Enumerative Combinatorics, 819th Meeting of the A.M.S., April 1985.

    Google Scholar 

  38. J. Labelle. Applications diverses de la théorie combinatoire des espèces de structures, Ann. Sc. Math. du Québec, 7, no. 1, 1983, 59–94.

    MathSciNet  MATH  Google Scholar 

  39. J. Labelle. Quelques espèces sur les ensembles de petite cardinalité, Ann. Sc. Math. du Québec, 9, no. 1, 1985, 31–58.

    MathSciNet  MATH  Google Scholar 

  40. J. Labelle. On the Decomposition of Species, Rapport de recherche no. 14, UQAM, mai 1986.

    Google Scholar 

  41. A. Longtin. Une combinatoire non-commutative pour l'étude des nombres sécants, (this volume).

    Google Scholar 

  42. P. Leroux et V. Strehl. Jacobi polynomials: combinatorics of the basic identities, Discrete Math., 57, 1985, 167–187.

    Article  MathSciNet  MATH  Google Scholar 

  43. P. Leroux et G. Viennot. Combinatorial Resolution of Systems of differential Equations. I. Ordinary differential Equations, (this volume).

    Google Scholar 

  44. G. Pólya. Kombinatorische Anzahbestimmungen fur Gruppen, Graphen und chemische Verbindungen, Acta Math. 68, 1937, 145–254.

    Article  MathSciNet  MATH  Google Scholar 

  45. R. C. Read. A note on the number of functional digraphs. Math. Ann., 143, 1961, 109–110.

    Article  MathSciNet  MATH  Google Scholar 

  46. J. H. Redfield. The theory of group-reduced distributions. Amer. J. Math., 49, 1927, 443–455.

    Article  MathSciNet  MATH  Google Scholar 

  47. R. W. Robinson. Enumeration of nonseparable Graphs, J. Comb. Theory, Series B, 9, 1970, 327–356.

    Article  MATH  Google Scholar 

  48. T. J. Stieltjes. Sur une généralisation de la série de Lagrange, Oeuvre Complète, vol. 1, P. Noordhoff, Groningen, 1914, 445–450.

    Google Scholar 

  49. T. R. S. Walsh. Counting unlabelled three-connected and homeomorphically irreducible two-connected Graphs, J. Comb. Theory, Series B, 32, 1982, 12–32.

    Article  MathSciNet  MATH  Google Scholar 

  50. Y. N. Yeh. On the Combinatorial Species of Joyal, Ph.D. Thesis, State University of New York at Buffalo, 1985.

    Google Scholar 

  51. Y. N. Yeh. The calculus of virtual species andK-species, (this volume).

    Google Scholar 

  52. D. Zeilberger. Personal communication (June 10, 1985).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Gilbert Labelle Pierre Leroux

Rights and permissions

Reprints and permissions

Copyright information

© 1986 Springer-Verlag

About this paper

Cite this paper

Labelle, G. (1986). Some new computational methods in the theory of species. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072517

Download citation

  • DOI: https://doi.org/10.1007/BFb0072517

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17207-9

  • Online ISBN: 978-3-540-47402-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics