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- W2034875983 abstract "Abstract Let R = k [ x 1 ,…, x n ], where k is a field. The path ideal (of length t ≥ 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 show that R/I t (C n ) is S r if and only if it is Cohen-Macaulay or $lceil frac{n}{n-t-1}rceilgeq r+3$ . In addition, we prove that R/I t (C n ) is Gorenstein if and only if n = t or 2 t + 1. Also, we determine all ordinary and symbolic powers of I t (C n ) which are Cohen-Macaulay. Finally, we prove that I t (C n ) has a linear resolution if and only if t ≥ n − 2." @default.
- W2034875983 created "2016-06-24" @default.
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- W2034875983 date "2014-08-26" @default.
- W2034875983 modified "2023-09-25" @default.
- W2034875983 title "GORENSTEIN AND Sr PATH IDEALS OF CYCLES" @default.
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- W2034875983 doi "https://doi.org/10.1017/s0017089514000111" @default.
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