2015/05/28 by Juhnke-Kubitzke, Martina, Katthän, Lukas, Madani, Sara Saeedi · 1 citation
#05E40 (Primary) #06A11 #13D02 #13F55 (Secondary) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1505.07581
Given finite posets P and Q, we consider a specific ideal L(P,Q), whose minimal monomial generators correspond to order-preserving maps ϕ: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. Precise formulas are obtained 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 and having a linear resolution. We also give a partial characterization for Golod property of L(P,Q). Using those results, we derive applications for other important classes of monomial ideals, such as initial ideals of determinantal ideals and multichain ideals.