GORENSTEIN AND Sr PATH IDEALS OF CYCLES
Glasgow mathematical journal, Tome 57 (2015) no. 1, pp. 7-15
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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.
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
@article{10_1017_S0017089514000111,
author = {KIANI, DARIUSH and MADANI, SARA SAEEDI and TERAI, NAOKI},
title = {GORENSTEIN {AND} {Sr} {PATH} {IDEALS} {OF} {CYCLES}},
journal = {Glasgow mathematical journal},
pages = {7--15},
year = {2015},
volume = {57},
number = {1},
doi = {10.1017/S0017089514000111},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000111/}
}
TY - JOUR AU - KIANI, DARIUSH AU - MADANI, SARA SAEEDI AU - TERAI, NAOKI TI - GORENSTEIN AND Sr PATH IDEALS OF CYCLES JO - Glasgow mathematical journal PY - 2015 SP - 7 EP - 15 VL - 57 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000111/ DO - 10.1017/S0017089514000111 ID - 10_1017_S0017089514000111 ER -
%0 Journal Article %A KIANI, DARIUSH %A MADANI, SARA SAEEDI %A TERAI, NAOKI %T GORENSTEIN AND Sr PATH IDEALS OF CYCLES %J Glasgow mathematical journal %D 2015 %P 7-15 %V 57 %N 1 %U http://geodesic.mathdoc.fr/articles/10.1017/S0017089514000111/ %R 10.1017/S0017089514000111 %F 10_1017_S0017089514000111
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