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The Dedekind-Mertens formula and determinantal rings |
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| Authors: | Winfried Bruns Anna Guerrieri |
| Institution: | Universität Osnabrück, FB Mathematik/Informatik, 49069 Osnabrück, Germany ; Università di L'Aquila, Dip. di Matematica, Via Vetoio, Coppito, 67010 L'Aquila, Italy |
| 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  Cohen-Macaulay modules over the determinantal rings ![$KX]/I_2(X)$](http://www.ams.org/proc/1999-127-03/S0002-9939-99-04535-9/gif-abstract/img2.gif){kind=small} . |
| Keywords: | Dedekind--Mertens formula initial ideal determinantal ring Cohen--Macaulay module |
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