Classes of cut ideals and their Betti numbers

被引：0
作者：
Jürgen Herzog
Masoomeh Rahimbeigi
Tim Römer
机构：
[1] Universität Duisburg-Essen,Fachbereich Mathematik
[2] Universität Osnabrück,Institut für Mathematik
来源：
São Paulo Journal of Mathematical Sciences | 2023年 / 17卷
关键词：
Cut sets; Monomial ideals; Number of generators; Betti numbers; Cohen–Macaulay type; Powers of ideals; Primary 05E40; 13C99; Secondary 13F20; 13H10;
D O I：
暂无
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学科分类号：
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.
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页码：172 / 187
页数：15
相关论文
共 24 条
[1]  
Auslander M(1961)Modules over unramified regular local rings Illinois J. Math. 5 631-647
[2]  
Böröczky KJ(2014)On sumsets and convex hull Discrete Comput. Geom. 52 705-729
[3]  
Santos F(1994)Applications of cut polyhedra I J. Comput. Appl. Math. 55 191-216
[4]  
Serra O(1994)Applications of cut polyhedra II J. Comput. Appl. Math. 55 217-247
[5]  
Deza M(2011)Cut ideals of Michigan Math. J. 60 705-714
[6]  
Laurent M(2019)-minor-free graphs are generated by quadrics Math. Z. 291 999-1014
[7]  
Deza M(2022)The relevance of Freiman’s theorem for combinatorial commutative algebra J. Pure Appl. Algebra 226 22-565
[8]  
Laurent M(2009)Seminormality, canonical modules, and regularity of cut polytopes J. Commut. Algebra 1 547-1166
[9]  
Engström A(2010)Properties of cut ideals associated to ring graphs Discrete Math. 310 1160-129
[10]  
Herzog J(2014)Normality of cut polytopes of graphs is a minor closed property Eur. J. Combin. 38 122-970
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