Classes of cut ideals and their Betti numbers

被引：2

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

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