On the matroidal path ideals

被引：0

作者：

Khashyarmanesh, Kazem ^{[1
]}

Nasernejad, Mehrdad ^{[1
]}

Qureshi, Ayesha Asloob ^{[2
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Pure Math, POB 1159-91775, Mashhad, Iran

[2] Sabanci Univ, Fac Engn & Nat Sci Orta Mahalle, TR-34956 Istanbul, Turkey

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2023年 / 22卷 / 11期

关键词：

Veronese ideals; depth of powers of ideals; matroids; polymatroidal ideals; complete multipartite graphs; MONOMIAL IDEALS; POWERS; DEPTH;

D O I：

10.1142/S0219498823502274

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove that the set of all paths of a fixed length in a complete multipartite graph is the bases of a matroid. Moreover, we discuss the Cohen-Macaulayness and depth of powers of t-path ideals of a complete multipartite graph.

引用

页数：17

共 23 条

[1] ON THE WEAKLY POLYMATROIDAL PROPERTY OF THE EDGE IDEALS OF HYPERGRAPHS [J].

Asghar, Rahim Rahmati ;

Yassemi, Siamak .

COMMUNICATIONS IN ALGEBRA, 2014, 42 (03) :1011-1021

[2] Monomial localizations and polymatroidal ideals [J].

Bandari, Somayeh ;

Herzog, Juergen .

EUROPEAN JOURNAL OF COMBINATORICS, 2013, 34 (04) :752-763

[3] Path ideals of rooted trees and their graded Betti numbers [J].

Bouchat, Rachelle R. ;

Ha, Huy Tai ;

O'Keefe, Augustine .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2011, 118 (08) :2411-2425

[4] ASYMPTOTIC NATURE OF THE ANALYTIC SPREAD [J].

BRODMANN, M .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1979, 86 (JUL) :35-39

[5] Depths and Cohen-Macaulay properties of path ideals [J].

Campos, Daniel ;

Gunderson, Ryan ;

Morey, Susan ;

Paulsen, Chelsey ;

Polstra, Thomas .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2014, 218 (08) :1537-1543

[6] SOME ARITHMETIC PROPERTIES OF MATROIDAL IDEALS [J].

Chiang-Hsieh, Hung-Jen .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (03) :944-952

[7] M-sequences, graph ideals, and ladder ideals of linear type [J].

Conca, A ;

De Negri, E .

JOURNAL OF ALGEBRA, 1999, 211 (02) :599-624

[8]

Conca Aldo., 2003, Collect. Math, V54, P137

[9]

Edmonds J., 1970, Combinatorial struc- tures and their applications, P69

[10] Algebraic Properties of the Path Ideal of a Tree [J].

He, Jing ;

Van Tuyl, Adam .

COMMUNICATIONS IN ALGEBRA, 2010, 38 (05) :1725-1742

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