On Subdivision Posets of Cyclic Polytopes

@article{Edelman2000OnSP,
  title={On Subdivision Posets of Cyclic Polytopes},
  author={Paul H. Edelman and J{\"o}rg Rambau and Victor Reiner},
  journal={Eur. J. Comb.},
  year={2000},
  volume={21},
  pages={85-101}
}
There are two related poset structures, the higher Stasheff–Tamari orders, on the set of all triangulations ofthe cyclicd polytope withn vertices. In this paper it is shown that both of them have the homotopy type of a sphere of dimension n− d − 3. Moreover, we resolve positively a new special case of the Generalized Baues Problem : the Baues poset of all polytopal decompositions of a cyclic polytope of dimension d ≤ 3 has the homotopy type of a sphere of dimension− d − 2. 

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