Sequentially cohen-Macaulay path ideals of cycles

Sara Saeedi Madani; Dariush Kiani; Naoki Terai

Sequentially cohen-Macaulay path ideals of cycles

Sara Saeedi Madani, Dariush Kiani, Naoki Terai

Research output: Contribution to journal › Article › peer-review

Abstract

Let R = k[x₁, . . . , 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 I_t(G), whose generators correspond to the directed paths of length t in G. Let C_nbe an n-cycle. We determine when I _t(C_n) is unmixed. Moreover, We show that R/I _t(C_n) is sequentially Cohen-Macaulay if and only if n = t or t + 1 or 2t + 1.

Original language	English
Pages (from-to)	353-363
Number of pages	11
Journal	Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Volume	54
Issue number	4
Publication status	Published - 2011
Externally published	Yes

Keywords

Path ideals
Sequentially cohen-macaulay

ASJC Scopus subject areas

Mathematics(all)

Cite this

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N2 - 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.

AB - 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.

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KW - Sequentially cohen-macaulay

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Sequentially cohen-Macaulay path ideals of cycles

Abstract

Keywords

ASJC Scopus subject areas

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