The principal result is a primary decomposition of ideals generated by the
(2x2)-subpermanents of a generic matrix. These permanental ideals almost always
have embedded components and their minimal primes are of three distinct
heights. Thus the permanental ideals are almost never Cohen-Macaulay, in
contrast with determinantal ideals.Comment: 13 page

Laubenbacher, R.

Swanson, I.

English

arXiv

We show that the (2 \Theta 2)-subpermanents of a generic matrix generate an ideal  whose height, unmixedness, primary decomposition, the number and structure of the minimal  components, resolutions, radical, integral closure and Grobner bases all depend on the  characteristic of the underlying subfield: if the characteristic of the subfield is two, this ideal  is the determinantal ideal for which all of these properties are already well-known. We show  that as long as the characteristic of the subfield is not two, the results are in marked contrast  with those for the determinantal ideals

Reinhard C. Laubenbacher

Irena Swanson

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Permanental Ideals

http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.7.3654

Permanental Ideals

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