We give a combinatorial proof of the Dedekind-Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank $1$ Cohen-Macaulay modules over the determinantal rings $K[X]/I_2(X)$.

The Dedekind-Mertens formula and determinantal rings

GUERRIERI, ANNA
1999-01-01

Abstract

We give a combinatorial proof of the Dedekind-Mertens formula by computing the initial ideal of the content ideal of the product of two generic polynomials. As a side effect we obtain a complete classification of the rank $1$ Cohen-Macaulay modules over the determinantal rings $K[X]/I_2(X)$.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11697/21081
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