Classes of cut ideals and their Betti numbers

被引：0

作者：

Herzog, Jurgen ^{[1
]}

Rahimbeigi, Masoomeh

Roemer, Tim ^{[2
]}

机构：

[1] Univ Duisburg Essen, Fachbereich Math, Campus Essen, D-45117 Essen, Germany

[2] Univ Osnabruck, Inst Math, D-49069 Osnabruck, Germany

来源：

SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | 2023年 / 17卷 / 01期

关键词：

Cut sets; Monomial ideals; Number of generators; Betti numbers; Cohen-Macaulay type; Powers of ideals; GRAPHS;

D O I：

10.1007/s40863-022-00325-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study monomial cut ideals associated to a graph G, which are a monomial analogue of toric cut ideals as introduced by Sturmfels and Sullivant. Primary decompositions, projective dimensions, and Castelnuovo-Mumford regularities are investigated if the graph can be decomposed as 0-clique sums and disjoint union of subgraphs. The total Betti numbers of a cycle are computed. Moreover, we classify all Freiman ideals among monomial cut ideals.

引用

页码：172 / 187

页数：16

共 21 条

[1] Auslander M., 1961, ILLINOIS J MATH, V5, P631, DOI 10.1215/ijm/1255631585
[2] On Sumsets and Convex Hull
Boeroeczky, Karoly J.
Santos, Francisco
Serra, Oriol
[J]. DISCRETE & COMPUTATIONAL GEOMETRY, 2014, 52 (04) : 705 - 729
[3] CoCoATeam, COCOA SYST DOING COM
[4] DEZA M, 1994, J COMPUT APPL MATH, V55, P191, DOI 10.1016/0377-0427(94)90020-5
[5] Deza M., 1997, Algorithms and Combinatorics, V46, P282, DOI [10.1007/978-3-642-04295-9, DOI 10.1007/978-3-642-04295-9]
[6] Diestel R., 2016, GRAPH THEORY, V173, DOI DOI 10.1007/978-3-662-53622-3
[7] Cut Ideals of K4-Minor Free Graphs Are Generated by Quadrics
Engstrom, Alexander
[J]. MICHIGAN MATHEMATICAL JOURNAL, 2011, 60 (03) : 705 - 714
[8] Freiman G., 1973, Translations of Mathematical Mono graphs, V37
[9] Herzog, 1974, HABILITATION
[10] The relevance of Freiman's theorem for combinatorial commutative algebra
Herzog, Juergen
Hibi, Takayuki
Zhu, Guangjun
[J]. MATHEMATISCHE ZEITSCHRIFT, 2019, 291 (3-4) : 999 - 1014

← 1 2 3 →