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• W1656241735 abstract "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 Bjorner 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." @default.
• W1656241735 created "2016-06-24" @default.
• W1656241735 creator A5033218989 @default.
• W1656241735 creator A5079062539 @default.
• W1656241735 date "2007-07-19" @default.
• W1656241735 modified "2023-09-27" @default.
• W1656241735 title "Pretty clean monomial ideals and linear quotients" @default.
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• W1656241735 hasPublicationYear "2007" @default.
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