Transactions of the American Mathematical Society

Author(s): George A. Kirkup
Journal: Trans. Amer. Math. Soc. 360 (2008), 3751-3770.
MSC (2000): Primary 13P10
Posted: February 27, 2008
Retrieve article in: PDF DVI PostScript

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.

[AT]: N. Alon and M. Tarsi, A nowhere-zero point in linear mappings, Combinatorica 9 (1989), no. 4, 393-395. MR 1054015 (92a:11147)
[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 (95k:11160)
[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 Laubenbacher and Irena Swanson, Permanental ideals, J. Symbolic Computation 30 (2000), 195-295. MR 1777172 (2001i:13039)
[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, 2002. MR 1925796 (2003i:13037)
[Yu]: Yang Yu, The permanent rank of a matrix, J. Combin. Theory Ser. A 85 (1999), no. 2, 237-242. MR 1673948 (99j:15013)

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13P10

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

DOI: 10.1090/S0002-9947-08-04340-7
PII: S 0002-9947(08)04340-7
Received by editor(s): October 2, 2005
Received by editor(s) in revised form: May 21, 2006
Posted: February 27, 2008
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6850(e) ISSN 0002-9947(p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2008, American Mathematical Society Privacy Statement		Search the AMS