Pretty clean monomial ideals and linear quotients
| dc.creator | Jahan, Ali Soleyman | |
| dc.creator | Zheng, Xinxian | |
| dc.date | 2007-07-19 | |
| dc.date.accessioned | 2026-07-07T08:19:14Z | |
| dc.date.available | 2026-07-07T08:19:14Z | |
| dc.description | We study basic properties of monomial ideals with linear quotients. It is shown that if the monomial ideal $I$ has linear quotients, then the squarefree part of $I$ and each component of $I$ as well as $\mm I$ have linear quotients, where $\mm$ is the graded maximal ideal of the polynomial ring. As an analogy to the Rearrangement Lemma of Björner and Wachs we also show that for a monomial ideal with linear quotients the admissible order of the generators can be chosen degree increasingly. As a generalization of the facet ideal of a forest, we define monomial ideals of forest type and show that they are pretty clean. This result recovers a recent result of Tuly and Villarreal about the shellability of a clutter with the free vertex property. As another consequence of this result we show that if $I$ is a monomial ideal of forest type, then Stanley's conjecture on Stanley decomposition holds for $S/I$. We also show that a clutter is totally balanced if and only if it has the free vertex property. | |
| dc.identifier | https://arxiv.org/abs/0707.2914 | |
| dc.identifier | http://arxiv.org/abs/0707.2914 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134697 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13F20; 13F55; 13A30; 16W70 | |
| dc.title | Pretty clean monomial ideals and linear quotients | |
| dc.type | text |