The stable set of associated prime ideals of a polymatroidal ideal
The associated prime ideals of powers of polymatroidal ideals are studied, including the stable set of associated prime ideals of this class of ideals. It is shown that polymatroidal ideals have the persistence property and for transversal polymatroids and polymatroidal ideals of Veronese type the index of stability and the stable set of associated ideals is determined explicitly.
KeywordsAssociated prime ideals Polymatroidal ideals Analytic spread
This paper was partially written during the visit of the second and third author at the Universität Duisburg-Essen, Campus Essen. The second author wants to thank The Abdus Salam International Centre for Theoretical Physics (ICTP), Trieste, Italy for supporting her. The third author was supported by a Romanian grant awarded by UEFISCDI, project number 83/2010, PNII-RU code TE_46/2010, program Human Resources, “Algebraic modeling of some combinatorial objects and computational applications”.
- 4.Bruns, W., Herzog, J.: Cohen–Macaulay Rings, Revised edn. Cambridge University Press, Cambridge (1996) Google Scholar
- 6.CoCoATeam: CoCoA: a system for doing computations in commutative algebra. Available at http://cocoa.dima.unige.it
- 11.Greuel, G.M., Pfister, G., Schönemann, H.: Singular 2.0. A computer algebra system for polynomial computations. Centre for Computer Algebra, University of Kaiserslautern (2001). http://www.singular.uni-kl.de
- 14.Herzog, J., Hibi, T.: Monomial Ideals. GTM, vol. 260. Springer, Berlin (2010) Google Scholar
- 18.Martinez-Bernal, J., Morey, S., Villarreal, R.H.: Associated primes of powers of edge ideals. arXiv:1103.0992v3
- 19.Morey, S., Villarreal, R.H.: Edge ideals: algebraic and combinatorial properties. arXiv:1012.5329v3