Journal of Algebraic Combinatorics

, Volume 10, Issue 2, pp 173–188 | Cite as

Combinatorics of Necklaces and “Hermite Reciprocity”

  • A. Elashvili
  • M. Jibladze
  • D. Pataraia


Combinatorial proof of an explicit formula for dimensions of spaces of semi-invariants of regular representations of finite cyclic groups is obtained. Using bicolored necklaces, a certain reciprocity law following from this formula is also derived combinatorially.

partition necklace semi-invariant reciprocity 


  1. 1.
    G.E. Andrews, “The theory of partitions,” Encyclopedia of Mathematics and Its Applications, G.-C. Rota, (Ed.), Addison-Wesley, Reading, MA, 1976, Vol.2.Google Scholar
  2. 2.
    N. Bourbaki, Groupes et algébres de Lie, Hermann, Paris, 1971–1972.Google Scholar
  3. 3.
    A. Elashvili and M. Jibladze, “Hermite Reciprocity for regular representations of cyclic groups,” Indag Mathem., N.S., 9(2), 1998, 233–238.Google Scholar
  4. 4.
    Higher Transcendental Functions, Bateman Manuscript Project, A.Erd´elyi (dir.), McGraw-Hill, New York, 1955.Google Scholar
  5. 5.
    S. Ramanujan, “On certain trigonometrical sums and their applications in the theory of numbers,” Trans.Camb.Phil.Soc., XXII(13) (1918), 259–276Google Scholar
  6. 6.
    T.A. Springer, Invariant theory, Lecture Notes in Math., Vol.585, Springer-Verlag, Berlin and New York, 1977.Google Scholar
  7. 7.
    R. Stanley, Enumerative Combinatorics, Vol.I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.Google Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • A. Elashvili
    • 1
  • M. Jibladze
    • 1
  • D. Pataraia
    • 1
  1. 1.A. Razmadze Mathematical Institute of theGeorgian Academy of SciencesTbilisiRepublic of Georgia

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