Sara Saeedi Madani, Dariush Kiani and Naoki Terai: Sequentially Cohen-Macaulay path ideals of cycles, p.353-363

Abstract:

Let $R=k[x_{1},\ldots,x_{n}]$, where $k$ is a field. The path ideal (of length $t\geq 2$) 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 $C_{n}$ be an n-cycle. We determine when $I_{t}(C_{n})$ is unmixed. Moreover, We show that $R/I_{t}(C_{n})$ is sequentially Cohen-Macaulay if and only if $n=t$ or $t+1$ or $2t+1$.

Key Words: Path ideals, sequentially Cohen-Macaulay.

2000 Mathematics Subject Classification: Primary: 13D02;
Secondary: 13F55, 05C75, 05C38.

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