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Jacobians of Symmetric Polynomials
Alain Lascoux1 and Piotr Pragacz2
1CNRS, Institut Gaspard Monge, Université de Marne-la-Vallee, 77454 Marne-la-Vallée Cedex France
alain.lascoux@univ-mlv.fr
2Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00950 Warsaw, Poland
pragacz@impan.gov.pl
Annals of Combinatorics 6 (2) p.169-172 June, 2002
AMS Subject Classification: 05E05, 26B10
Abstract:
We give the Jacobian of any family of complete symmetric functions, or of power sums, in a finite number of variables.
Keywords: Jacobians, symmetric functions

References:

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2. I.G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford University Press, Oxford, 2nd Edition, 1995.

3. Capt. MacMahon, Operators in the theory of seminvariants, Quart. J. Math. 20 (1885) 362– 365.

4. T. Muir, History of the Theory of Determinants, Vol. III, reprinted by Dover, 1960.

5. R.F. Scott, On some alternating functions of n variables, Messenger of Math. 11 (1882) 98–103.

6. J.J. Sylvester, Note on Capt. MacMahon’s transformation of the theory of invariants, Messenger of Math. 14 (1884) 163–165.