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- W2890417146 abstract "For each squarefree monomial ideal $Isubset S = k[x_{1},ldots, x_{n}] $, we associate a simple graph $G_I$ by using the first linear syzygies of $I$. In cases, where $G_I$ is a cycle or a tree, we show the following are equivalent: (a) $ I $ has a linear resolution (b) $ I $ has linear quotients (c) $ I $ is a variable-decomposable ideal In addition, with the same assumption on $G_I$, we characterize all monomial ideals with a linear resolution. Using our results, we characterize all Cohen-Macaulay codimension $2$ monomial ideals with a linear resolution. As an other application of our results, we also characterize all Cohen-Macaulay simplicail complexes in cases that $G_{Delta}cong G_{I_{Delta^{vee}}}$ is a cycle or a tree." @default.
- W2890417146 created "2018-09-27" @default.
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- W2890417146 creator A5079062539 @default.
- W2890417146 date "2018-09-01" @default.
- W2890417146 modified "2023-09-27" @default.
- W2890417146 title "Linear syzygy graph and linear resolution" @default.
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