HOMOLOGICAL INVARIANTS OF CAMERON-WALKER GRAPHS

被引：5

作者：

Hibi, Takayuki ^{[1
]}

Kanno, Hiroju ^{[1
]}

Kimura, Kyouko ^{[2
]}

Matsuda, Kazunori ^{[3
]}

Van Tuyl, Adam ^{[4
]}

机构：

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Dept Pure & Appl Math, Suita, Osaka 5650871, Japan

[2] Shizuoka Univ, Fac Sci, Dept Math, Suruga Ku, 836 Ohya, Shizuoka 4228529, Japan

[3] Kitami Inst Technol, Kitami, Hokkaido 0908507, Japan

[4] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4L8, Canada

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2021年 / 374卷 / 09期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Edge ideal; dimension; depth; Castelnuovo-Mumford regularity; h-polynomials; EDGE IDEALS; INDEPENDENCE; REGULARITY; NUMBERS;

D O I：

10.1090/tran/8416

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite simple connected graph on [n] and R = K[x(1), ..., x(n)] the polynomial ring in n variables over a field K. The edge ideal of G is the ideal I(G) of R which is generated by those monomials x(i)x(j) for which {i, j} is an edge of G. In the present paper, the possible tuples (n, depth(R/I(G)), reg(R/I(G)), dim R/I(G), deg h(R/I(G))), where deg h(R/I(G)) is the degree of the h-polynomial of R/I(G), arising from Cameron-Walker graphs on [n] will be completely determined.

引用

页码：6559 / 6582

页数：24

共 50 条

[1] Algebraic study on Cameron-Walker graphs
Hibi, Takayuki
Higashitani, Akihiro
Kimura, Kyouko
O'Keefe, Augustine B.
[J]. JOURNAL OF ALGEBRA, 2015, 422 : 257 - 269
[2] Regularity, matchings and Cameron-Walker graphs
Trung, Tran Nam
[J]. COLLECTANEA MATHEMATICA, 2020, 71 (01) : 83 - 91
[3] Regularity and a-invariant of Cameron-Walker graphs
Hibi, Takayuki
Kimura, Kyouko
Matsuda, Kazunori
Tsuchiya, Akiyoshi
[J]. JOURNAL OF ALGEBRA, 2021, 584 : 215 - 242
[4] Regularity of symbolic powers of edge ideals of Cameron-Walker graphs
Seyed Fakhari, S. A.
[J]. COMMUNICATIONS IN ALGEBRA, 2020, 48 (12) : 5215 - 5223
[5] Foundations of Sheaves on Graphs and Their Homological Invariants
Friedman, Joel
[J]. MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2015, 233 (1100) : 1 - +
[6] Regularity, matchings and Cameron–Walker graphs
Tran Nam Trung
[J]. Collectanea Mathematica, 2020, 71 : 83 - 91
[7] Certain homological invariants of bipartite kneser graphs
Kumar, Ajay
Singh, Pavinder
Verma, Rohit
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2022, 21 (10)
[8] HOMOLOGICAL INVARIANTS OF RINGS
GULLIKSE.TH
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 16 (03): : 532 - &
[9] Powers of sums and their homological invariants
Nguyen, Hop D.
Thanh Vu
[J]. JOURNAL OF PURE AND APPLIED ALGEBRA, 2019, 223 (07) : 3081 - 3111
[10] Homological invariants of determinantal thickenings
Raicu, Claudiu
[J]. BULLETIN MATHEMATIQUE DE LA SOCIETE DES SCIENCES MATHEMATIQUES DE ROUMANIE, 2017, 60 (04): : 425 - 446

← 1 2 3 4 5 →