Strong persistence and associated primes of powers of monomial ideals

References

• Al-Ayyoub, I., Nasernejad, M., Roberts, L. G. (2019). Normality of cover ideals of graphs and normality under some operations. Results Math. 74(140):26. DOI: 10.1007/s00025-019-1068-x.
   Google Scholar
• Bayati, S., Herzog, J., Rinaldo, G. (2012). On the stable set of associated prime ideals of a monomial ideal. Arch. Math. 98:213–217. DOI: 10.1007/s00013-012-0368-0.
   Web of Science ®Google Scholar
• Bela, E., Favacchio, G., Tran, N. (2021). In the shadows of a hypergraph: Looking for associated primes of powers of square-free monomial ideals. J. Algebraic Comb. 53:11–29. DOI: 10.1007/s10801-019-00915-5.
   Web of Science ®Google Scholar
• Brodmann, M. (1979). Asymptotic stability of Ass(M/InM) . Proc. Amer. Math. Soc. 74:16–18.
   Google Scholar
• Brodmann, M. (1979). The asymptotic nature of the analytic spread. Math. Proc. Cambridge Philos. Soc. 86:35–39. DOI: 10.1017/S030500410000061X.
   Web of Science ®Google Scholar
• Carlini, E., Hà, H. T., Harbourne, B., Van Tuyl, A. (2020). Ideals of Powers and Powers of Ideals, Intersecting Algebra, Geometry, and Combinatorics, Lecture Notes of the Unione Matematica Italiana, Vol. 7172. Cham: Springer.
   Google Scholar
• Francisco, C. A., Hà, H. T., Van Tuyl, A. (2010). Associated primes of monomial ideals and odd holes in graphs. J. Algebraic Comb. 32:287–301. DOI: 10.1007/s10801-010-0215-y.
   Web of Science ®Google Scholar
• Francisco, C. A., Hà, H. T., Van Tuyl, A. (2010). A conjecture on critical graphs and connections to the persistence of associated primes. Discrete Math. 310:2176–2182. DOI: 10.1016/j.disc.2010.04.014.
   Web of Science ®Google Scholar
• Francisco, C. A., Hà, H. T., Van Tuyl, A. (2011). Colorings of hypergraphs, perfect graphs, and associated primes of powers of monomial ideals. J. Algebra 331:224–242.
   Web of Science ®Google Scholar
• Grayson, D. R., Stillman, M. E. Macaulay 2, a software system for research in algebraic geometry. Available at: http://www.math.uiuc.edu/Macaulay2/.
   Google Scholar
• Herzog, J., Hibi, T. (2005). The depth of powers of an ideal. J. Algebra 291:534–550. DOI: 10.1016/j.jalgebra.2005.04.007.
   Web of Science ®Google Scholar
• Herzog, J., Hibi, T. (2011). Monomial Ideals, GTM., Vol. 260. Berlin:Springer.
   Google Scholar
• Herzog, J., Hibi, T., Trung, N. V. (2007). Symbolic Powers of Monomial Ideals and Vertex Cover Algebras. Adv. Math. 210:304–322. DOI: 10.1016/j.aim.2006.06.007.
   Web of Science ®Google Scholar
• Herzog, J., Mafi, A. (2018). Stability properties of powers of ideals in regular local rings of small dimension. Pacific J. Math. 295:31–41. DOI: 10.2140/pjm.2018.295.31.
   Web of Science ®Google Scholar
• Herzog, J., Qureshi, A. A. (2015). Persistence and stability properties of powers of ideals. J. Pure Appl. Algebra 219:530–542. DOI: 10.1016/j.jpaa.2014.05.011.
   Web of Science ®Google Scholar
• Herzog, J., Rauf, A., Vladoiu, M. (2013). The stable set of associated prime ideals of a polymatroidal ideal. J. Algebraic Comb. 37:289–312. DOI: 10.1007/s10801-012-0367-z.
   Web of Science ®Google Scholar
• Kaiser, T., Stehlik, M., Skrekovski, R. (2014). Replication in critical graphs and the persistence of monomial ideals. J. Comb. Theory Ser. A 123:239–251. DOI: 10.1016/j.jcta.2013.12.005.
   Web of Science ®Google Scholar
• Karimi, S., Mafi, A. (2019). On stability properties of powers of polymatroidal ideals. Collect. Math. 70:357–365. DOI: 10.1007/s13348-018-0234-x.
   Web of Science ®Google Scholar
• Mafi, A. (2018). Ratliff-Rush ideal and reduction numbers. Commun. Algebra 46:1272–1276. DOI: 10.1080/00927872.2017.1344686.
   Web of Science ®Google Scholar
• Mafi, A., Naderi, D. (2021). A note on stability properties of powers of polymatroidal ideals. arXiv:2112.05918v1 [math.AC].
   Google Scholar
• Martinez-Bernal, J., Morey, S., Villarreal, R. H. (2012). Associated primes of powers of edge ideals. Collect. Math. 63:361–374. DOI: 10.1007/s13348-011-0045-9.
   Web of Science ®Google Scholar
• McAdam, S. (1983). Asymptotic prime divisors. Lecture Notes Mathematical, Vol. 1023. New York: Springer-Verlag.
   Google Scholar
• Morey, S., Villarreal, R. H. (2012). Edge ideals: Algebraic and Combinatorial properties. Berlin: De Gruyter, pp. 85–126.
   Google Scholar
• Nasernejad, M., Khashyarmanesh, K., Al-Ayyoub, I. (2019). Associated primes of powers of cover ideals under graph operations. Commun. Algebra 47:1985–1996.
   Web of Science ®Google Scholar
• Ratliff, L. J. (1976). On prime divisors of In, n large. Michigan. Math. J. 23:337–352.
   Google Scholar
• Reyes, E., Toledo, J. (2018). On the strong persistence property for monomial ideals. Bull. Math. Soc. Sci. Math. Roumanie 80:293–305.
   Google Scholar
• Simis, A., Vasconcelos, V. V., Villarreal, R. H. (1994). On the ideal theory of graphs. J. Algebra 167:389–416. DOI: 10.1006/jabr.1994.1192.
   Web of Science ®Google Scholar
• Villarreal, R. H. (1990). Cohen-Macaulay graphs. Manuscripta Math. 66:277–293. DOI: 10.1007/BF02568497.
   Web of Science ®Google Scholar
• Villarreal, R. H. (2008). Rees algebras and polyhedral cones of ideals of vertex covers of perfect graphs. J. Algebraic Comb. 27:293–305. DOI: 10.1007/s10801-007-0088-x.
   Web of Science ®Google Scholar