Combinatorics of Necklaces and “Hermite Reciprocity”
A. Elashvili
, M. Jibladze
and D. Pataraia
DOI: 10.1023/A:1018727630642
Abstract
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.
Pages: 173–188
Keywords: partition; necklace; semi-invariant; reciprocity
Full Text: PDF
References
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2. N. Bourbaki, Groupes et algébres de Lie, Hermann, Paris, 1971-1972.
3. A. Elashvili and M. Jibladze, “Hermite Reciprocity for regular representations of cyclic groups,” Indag Mathem., N.S., 9(2), 1998, 233-238.
4. Higher Transcendental Functions, Bateman Manuscript Project, A. Erdélyi (dir.), McGraw-Hill, New York, 1955.
5. S. Ramanujan, “On certain trigonometrical sums and their applications in the theory of numbers,” Trans. Camb. Phil. Soc., XXII(13) (1918), 259-276
6. T. A. Springer, Invariant theory, Lecture Notes in Math., Vol. 585, Springer-Verlag, Berlin and New York, 1977.
7. R. Stanley, Enumerative Combinatorics, Vol. I, Wadsworth & Brooks/Cole, Monterey, CA, 1986.