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Topic: [HM] Origin of name "symmetric function"
Replies: 3   Last Post: Aug 19, 2005 5:34 PM

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Heinz Lueneburg

Posts: 226
Registered: 12/3/04
Re: [HM] Origin of name "symmetric function"
Posted: Aug 15, 2005 10:36 AM
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Dear Christopher Baltus,

I can tell you that Lagrange does not use any name for the symmetric functions
in his big paper

Re/flexion sur la Re/solution alge/brique des e/quations. Nouveau Me/moires de
l'Acade/mie royale des Sciences et Belles-Lettres de Berlin, anne/es 1770 et
1771. Works vol. 3, 205-421.

Vandermonde uses the name "type de combinaison" mostly shortened to "type"
for homogeneous symmetric polynomials. He also uses the name "type partiel"
for the sum of monomials in n indeterminates, where the summands are the
images of one of the monomials under the powers of a permutation. (Gauss'
sums of his periods!)

Me/moire sur la re/solution des e/quations. Histoire de l'Acade/mie royale des
Sciences. Anne/e 1771. Paris 1774, 365-416. The paper was read before the
Academy in 1770.

Vandermonde was not yet "de l'Acade/mie" in 1770. That's why the paper was
not published in the Histoire of 1770.

So, you have to look for publications in the period from 1770 to 1799.

Concerning Vandermonde and Gausz, see

Henri Lebesgue, L'OEuvres mathe/matiques de Vandermonde. L'Enseignement de
mathe/matique I, 203--223, 1955

Heinz Lueneburg

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