Abstract
There are two related poset structures, the higher Stasheff-Tamari orders, on the set of all triangulations of the cyclic d polytope with n 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 n - d - 2.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 85-101 |
| Number of pages | 17 |
| Journal | European Journal of Combinatorics |
| Volume | 21 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2000 |
Bibliographical note
Funding Information:†The author was supported at MSRI in part by NSF grant #DMS 9022140. ‡The author was supported by a University of Minnesota McKnight-Land Grant Fellowship.