TY - JOUR
T1 - Gorenstein and Sr path ideals of cycles
AU - Kiani, Dariush
AU - Madani, Sara Seedi
AU - Terai, Naoki
N1 - Publisher Copyright:
© 2014 Glasgow Mathematical Journal Trust.
PY - 2015/1/25
Y1 - 2015/1/25
N2 - 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 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 n n-t-1 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.
AB - 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 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 n n-t-1 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.
KW - 05C38
KW - 05C75
KW - 13F55
KW - 2010 Mathematics Subject Classification 13D02
UR - http://www.scopus.com/inward/record.url?scp=84919820116&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84919820116&partnerID=8YFLogxK
U2 - 10.1017/S0017089514000111
DO - 10.1017/S0017089514000111
M3 - Article
AN - SCOPUS:84919820116
VL - 57
SP - 7
EP - 15
JO - Glasgow Mathematical Journal
JF - Glasgow Mathematical Journal
SN - 0017-0895
IS - 1
ER -