g-Elements, finite buildings and higher Cohen-Macaulay connectivity

@article{Swartz2006gElementsFB,
  title={g-Elements, finite buildings and higher Cohen-Macaulay connectivity},
  author={Ed Swartz},
  journal={J. Comb. Theory, Ser. A},
  year={2006},
  volume={113},
  pages={1305-1320}
}
Chari proved that if ∆ is a (d − 1)-dimensional simplicial complex with a convex ear decomposition, then h0 ≤ · · · ≤ hbd/2c [7]. Nyman and Swartz raised the problem of whether or not the corresponding g-vector is an M -vector [18]. This is proved to be true by showing that the set of pairs (ω, Θ), where Θ is a l.s.o.p. for k[∆], the face ring of ∆, and ω is a g-element for k[∆]/Θ, is nonempty whenever the characteristic of k is zero. Finite buildings have a convex ear decomposition. These… CONTINUE READING