@article {
author = {Nasernejad, M.},
title = {Asymptotic behaviour of associated primes of monomial ideals with combinatorial applications},
journal = {Journal of Algebra and Related Topics},
volume = {2},
number = {1},
pages = {15-25},
year = {2014},
publisher = {University of Guilan},
issn = {2345-3931},
eissn = {2382-9877},
doi = {},
abstract = {Let $R$ be a commutative Noetherian ring and $I$ be an ideal of $R$. We say that $I$ satisfies the persistence property if $\mathrm{Ass}_R(R/I^k)\subseteq \mathrm{Ass}_R(R/I^{k+1})$ for all positive integers $k\geq 1$, which $\mathrm{Ass}_R(R/I)$ denotes the set of associated prime ideals of $I$. In this paper, we introduce a class of square-free monomial ideals in the polynomial ring $R=K[x_1,\ldots,x_n]$ over field $K$ which are associated to unrooted trees such that if $G$ is a unrooted tree and $I_t(G)$ is the ideal generated by the paths of $G$ of length $t$, then $J_t(G):=I_t(G)^\vee$, where $I^\vee$ denotes the Alexander dual of $I$, satisfies the persistence property. We also present a class of graphs such that the path ideals generated by paths of length two satisfy the persistence property. We conclude this paper by giving a criterion for normally torsion-freeness of monomial ideals.},
keywords = {Monomial ideals,associated prime ideals,trees,paths},
url = {https://jart.guilan.ac.ir/article_57.html},
eprint = {https://jart.guilan.ac.ir/article_57_45c5e51de657c1dc081bfad7d1fc6b80.pdf}
}