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The ring of multisymmetric functions

Francesco Vaccarino (2005)

Annales de l’institut Fourier

We give a presentation (in terms of generators and relations) of the ring of multisymmetric functions that holds for any commutative ring R , thereby answering a classical question coming from works of F. Junker [J1, J2, J3] in the late nineteen century and then implicitly in H. Weyl book “The classical groups” [W].

The strong persistence property and symbolic strong persistence property

Mehrdad Nasernejad, Kazem Khashyarmanesh, Leslie G. Roberts, Jonathan Toledo (2022)

Czechoslovak Mathematical Journal

Let I be an ideal in a commutative Noetherian ring R . Then the ideal I has the strong persistence property if and only if ( I k + 1 : R I ) = I k for all k , and I has the symbolic strong persistence property if and only if ( I ( k + 1 ) : R I ( 1 ) ) = I ( k ) for all k , where I ( k ) denotes the k th symbolic power of I . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the...

Thom polynomials and Schur functions: the singularities I 2 , 2 ( - )

Piotr Pragacz (2007)

Annales de l’institut Fourier

We give the Thom polynomials for the singularities I 2 , 2 associated with maps ( , 0 ) ( + k , 0 ) with parameter k 0 . Our computations combine the characterization of Thom polynomials via the “method of restriction equations” of Rimanyi et al. with the techniques of Schur functions.

Thom polynomials and Schur functions: the singularities I I I 2 , 3 ( - )

Özer Öztürk (2010)

Annales Polonici Mathematici

We give a closed formula for the Thom polynomials of the singularities I I I 2 , 3 ( - ) in terms of Schur functions. Our computations combine the characterization of the Thom polynomials via the “method of restriction equations” of Rimányi et al. with the techniques of Schur functions.

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