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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