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Theorem of Poincare-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to stirling numbers

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References

  1. N. Bourbaki, Groupes et algèbres de Lie, chapitre 1, Hermann (1971).

    Google Scholar 

  2. K.T. Chen, Integration of paths, geometric invariants and a generalized Baker-Haussdorff formula, Annals Maths 65 (1957) 163–178.

    CrossRef  Google Scholar 

  3. J. Dixmier, Algèbres enveloppantes, Hermann (1974)

    Google Scholar 

  4. M. Fliess, D. Normand-Cyrot, Algèbres de Lie nilpotentes, intégrales itérées de K.T. Chen et formule de Baker-Campbell-Hausdorff, Lect. Notes Maths 920 (1982) 257–265.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. M. Fliess, C. Reutenauer, Picard-Vessiot theory of bilinear systems, IEEE 23rd Congress on Decision and Control, Proc., 1153–1157 (1983).

    Google Scholar 

  6. R.M. Hain, On the indecomposable elements of the bar construction, preprint (1985); see also: de Rham homotopy theory of complex algebraic varieties, manuscript (1984), appendix.

    Google Scholar 

  7. G.P. Hochschild, Basic theory of algebraic groups and Lie algebras, Springer Verlag (1981).

    Google Scholar 

  8. M. Lothaire, Combinatorics on words, Addison Wesley (1983)

    Google Scholar 

  9. D. Perrin, G. Viennot, A note on shuffle algebras (1981), manuscript.

    Google Scholar 

  10. R. Ree, Lie elements and an algebra associated with shuffles, Annals Maths 68 (1958) 210–220.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. C. Reutenauer, Point générique du plus petit groupe algébrique dont l'algèbre de Lie contient plusieurs matrices données, Comptes Rendus Acad. Sci. Paris 293 (1981) 577–580.

    MathSciNet  MATH  Google Scholar 

  12. C. Reutenauer, The shuffle algebra on the factors of a word is free, J. Combin. Theory 38 (1985) 48–57.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. J. Riordan, An introduction to combinatorial analysis, John Wiley 1967.

    Google Scholar 

  14. L. Solomon, On the Poincaré-Birkhoff-Witt theorem, J. Combin. Theory (A) 4 (1968) 363–375.

    CrossRef  MATH  Google Scholar 

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© 1986 Springer-Verlag

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Reutenauer, C. (1986). Theorem of Poincare-Birkhoff-Witt, logarithm and symmetric group representations of degrees equal to stirling numbers. In: Labelle, G., Leroux, P. (eds) Combinatoire énumérative. Lecture Notes in Mathematics, vol 1234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072520

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  • DOI: https://doi.org/10.1007/BFb0072520

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