Paul H. Edelman, Jörg Rambau, Victor Reiner
Published 1997-04-08Version 1
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 \emph{Generalized Baues Problem}: The Baues poset of all polytopal decompositions of a cyclic polytope of dimension $d \leq 3$ has the homotopy type of a sphere of dimension $n-d-2$.
Homotopy types of Hom complexes of graph homomorphisms whose codomains are square-free
Homotopy type of shellable $q$-complexes and their homology groups
New interpretations of the higher Stasheff--Tamari orders
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