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Polynômes multisymétriques

Abstract : This thesis deals with the study of the multi-symmetric polynomials : the invariants under the diagonal action of order r of the symmetric group Sn. The first chapter is devoted to generalities about these objects. Many formulae are given that connect the various remarkable families of multi-symmetric polynomials with one another. In the second chapter, it is presented an algorithm to compute a Gröbner basis of the ideal of relations between the elementary multi-symmetric polynomials. The third chapter deals with the connection between the multi-symmetric polynomials and the subvariety of products of linear forms inside the space of forms of degree n in r+1 variables. A Gröbner basis of the ideal of this subvariety is computed in the case n=4,r=3, and in the case n=4,r=2. Also, reformulations of the Foulkes-Howe Plethysm conjecture in terms of multi-symmetric polynomials is given. The last chapter is devoted to the study of explicit relations between the multi-symmetric functions of the roots and the coefficients of certain systems of polynomials equations with finitely many solutions.
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Contributor : Emmanuel Briand <>
Submitted on : Monday, January 27, 2003 - 7:02:38 PM
Last modification on : Thursday, January 7, 2021 - 4:12:56 PM
Long-term archiving on: : Tuesday, September 11, 2012 - 6:50:18 PM


  • HAL Id : tel-00002085, version 1


Emmanuel Briand. Polynômes multisymétriques. Mathématiques [math]. Université Rennes 1, 2002. Français. ⟨tel-00002085⟩



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