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 Cnbe an n-cycle. We determine when I t(Cn) is unmixed. Moreover, We show that R/I t(Cn) is sequentially Cohen-Macaulay if and only if n = t or t + 1 or 2t + 1.
|Number of pages||11|
|Journal||Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie|
|Publication status||Published - 2011|
- Path ideals
- Sequentially cohen-macaulay
ASJC Scopus subject areas