Sequentially Cohen-Macaulay path ideals of cycles
Bulletin mathématique de la Société des Sciences Mathématiques de Roumanie, 2011•JSTOR
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 Ic (G), whose generators correspond to the directed paths of
length t in G. Let Cn be an n-cycle. We determine when It (Cn) is unmixed. Moreover, We
show that R/It (Cn) is sequentially Cohen-Macaulay if and only if n= t or t+ 1 or 2t+ 1.
the monomial ideal, denoted by Ic (G), whose generators correspond to the directed paths of
length t in G. Let Cn be an n-cycle. We determine when It (Cn) is unmixed. Moreover, We
show that R/It (Cn) is sequentially Cohen-Macaulay if and only if n= t or t+ 1 or 2t+ 1.
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 Ic(G), whose generators correspond to the directed paths of length t in G. Let Cn be an n-cycle. We determine when It(Cn) is unmixed. Moreover, We show that R/It(Cn) is sequentially Cohen-Macaulay if and only if n = t or t + 1 or 2t + 1.
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