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- W4300787609 abstract "Let $R=k[x_{1},ldots,x_{n}]$, where $k$ is a field. The path ideal (of length $tgeq 2$) of a directed graph $G$ is the monomial ideal, denoted by $I_{t}(G)$, whose generators correspond to the directed paths of length $t$ in $G$. Let $Gamma$ be a directed rooted tree. We characterize all such trees whose path ideals are unmixed and Cohen-Macaulay. Moreover, we show that $R/I_{t}(Gamma)$ is Gorenstein if and only if the Stanley-Reisner simplicial complex of $I_{t}(Gamma)$ is a matroid." @default.
- W4300787609 created "2022-10-04" @default.
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- W4300787609 date "2015-04-22" @default.
- W4300787609 modified "2023-09-25" @default.
- W4300787609 title "Cohen-Macaulay and Gorenstein path ideals of trees" @default.
- W4300787609 doi "https://doi.org/10.48550/arxiv.1504.06001" @default.
- W4300787609 hasPublicationYear "2015" @default.
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