Classes of cut ideals and their Betti numbers
| Autor(en): | Herzog, Jurgen Rahimbeigi, Masoomeh Roemer, Tim |
Stichwörter: | Betti numbers; Cohen-Macaulay type; Cut sets; GRAPHS; Mathematics; Monomial ideals; Number of generators; Powers of ideals | Erscheinungsdatum: | 2022 | Herausgeber: | SPRINGER INT PUBL AG | Journal: | SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES | Zusammenfassung: | 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. |
ISSN: | 1982-6907 | DOI: | 10.1007/s40863-022-00325-9 |
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