Minimal primes over permanental ideals

Author:
George A. Kirkup

Journal:
Trans. Amer. Math. Soc. **360** (2008), 3751-3770

MSC (2000):
Primary 13P10

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 permanents of a generic matrix, and show that there are monomials in the ideal of maximal permanents of a 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.

**[AT]**N. Alon and M. Tarsi,*A nowhere-zero point in linear mappings*, Combinatorica**9**(1989), no. 4, 393–395. MR**1054015**, 10.1007/BF02125351**[BBLS]**R. D. Baker, J. Bonin, F. Lazebnik, and E. Shustin,*On the number of nowhere zero points in linear mappings*, Combinatorica**14**(1994), no. 2, 149–157. MR**1289069**, 10.1007/BF01215347**[GPS]**G.-M. Greuel, G. Pfister, and H. Schönemann,*SINGULAR 2.0*, A Computer Algebra System for Polynomial Computations, Centre for Computer Algebra, University of Kaiserslautern, 2001,`http://www.singular.uni-kl.de`.**[GS]**Daniel R. Grayson and Michael E. Stillman,*Macaulay 2, a software system for research in algebraic geometry*, Available at http://www.math.uiuc.edu/Macaulay2/.**[LS]**Reinhard C. Laubenbacher and Irena Swanson,*Permanental ideals*, J. Symbolic Comput.**30**(2000), no. 2, 195–205. MR**1777172**, 10.1006/jsco.2000.0363**[Stu]**Bernd Sturmfels,*Solving systems of polynomial equations*, CBMS Regional Conference Series in Mathematics, vol. 97, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2002. MR**1925796****[Yu]**Yang Yu,*The permanent rank of a matrix*, J. Combin. Theory Ser. A**85**(1999), no. 2, 237–242. MR**1673948**, 10.1006/jcta.1998.2904

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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.