2023/11/29 by Yang, Jay, Van Tuyl, Adam
#Combinatorics (math.CO) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2311.17806
A simplicial complex Δ is a virtually Cohen-Macaulay simplicial complex if its associated Stanley-Reisner ring S has a virtual resolution, as defined by Berkesch, Erman, and Smith, of length \rm codim(S). We provide a sufficient condition on Δ to be a virtually Cohen-Macaulay simplicial complex. We also introduce virtually shellable simplicial complexes, a generalization of shellable simplicial complexes. Virtually shellable complexes have the property that they are virtually Cohen-Macaulay, generalizing the well-known fact that shellable simplicial complexes are Cohen-Macaulay.