Geodesic
GORENSTEIN AND Sr PATH IDEALS OF CYCLES
Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 7-15

Voir la notice de l'article provenant de la source Cambridge University Press

Let R = k[x1,...,xn], where k is a field. The path ideal (of length t ≥ 2) of a directed graph G is the monomial ideal, denoted by It(G), whose generators correspond to the directed paths of length t in G. Let Cn be an n-cycle. We show that R/It(Cn) is Sr if and only if it is Cohen-Macaulay or $\lceil \frac{n}{n-t-1}\rceil\geq r+3$. In addition, we prove that R/It(Cn) is Gorenstein if and only if n = t or 2t + 1. Also, we determine all ordinary and symbolic powers of It(Cn) which are Cohen-Macaulay. Finally, we prove that It(Cn) has a linear resolution if and only if t ≥ n − 2.
DOI : 10.1017/S0017089514000111
Mots-clés : 13D02, 13F55, 05C75, 05C38 
KIANI, DARIUSH; MADANI, SARA SAEEDI; TERAI, NAOKI. GORENSTEIN AND Sr PATH IDEALS OF CYCLES. Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 7-15. doi: 10.1017/S0017089514000111
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