Algebraic properties of ideals of poset homomorphisms
Autor(en): | Juhnke-Kubitzke, Martina Katthaen, Lukas Madani, Sara Saeedi |
Stichwörter: | Betti numbers; GOLOD PROPERTY; Letterplace ideal; Mathematics; Monomial ideal; MONOMIAL IDEALS; Poset homomorphism; PRODUCTS; RINGS | Erscheinungsdatum: | 2016 | Herausgeber: | SPRINGER | Journal: | JOURNAL OF ALGEBRAIC COMBINATORICS | Volumen: | 44 | Ausgabe: | 3 | Startseite: | 757 | Seitenende: | 784 | Zusammenfassung: | Given finite posets P and Q, we consider a specific ideal L(P, Q), whose minimal monomial generators correspond to order-preserving maps phi : P -> Q. We study algebraic invariants of those ideals. In particular, sharp lower and upper bounds for the Castelnuovo-Mumford regularity and the projective dimension are provided. We obtain precise formulas for a large subclass of these ideals. Moreover, we provide complete characterizations for several algebraic properties of L(P, Q), including being Buchsbaum, Cohen-Macaulay, Gorenstein, Golod and having a linear resolution. |
ISSN: | 09259899 | DOI: | 10.1007/s10801-016-0687-5 |
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geprüft am 17.05.2024