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Transactions of the American Mathematical Society

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Minimal primes over permanental ideals


Author: George A. Kirkup
Journal: Trans. Amer. Math. Soc. 360 (2008), 3751-3770
MSC (2000): Primary 13P10
DOI: https://doi.org/10.1090/S0002-9947-08-04340-7
Published electronically: February 27, 2008
MathSciNet review: 2386244
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Abstract: In this paper we discuss minimal primes over permanental ideals of generic matrices. We give a complete list of the minimal primes over ideals of $ 3 \times 3$ permanents of a generic matrix, and show that there are monomials in the ideal of maximal permanents of a $ d \times (2d-1)$ matrix if the characteristic of the ground field is sufficiently large. We also discuss the Alon-Jaeger-Tarsi Conjecture, using our results and techniques to strengthen the previously known results.


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Additional Information

George A. Kirkup
Affiliation: Department of Mathematics, University of California, Berkeley, Berkeley, California 94720
Email: kirkup@math.berkeley.edu

DOI: https://doi.org/10.1090/S0002-9947-08-04340-7
Received by editor(s): October 2, 2005
Received by editor(s) in revised form: May 21, 2006
Published electronically: February 27, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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