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On Subdivision Posets of Cyclic Polytopes

Paul H. Edelman·Jörg Rambau·Victor Reiner
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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 \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 $n-d-2$.

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Paul H. Edelman, Jörg Rambau, Victor Reiner. 1997-04-08. On Subdivision Posets of Cyclic Polytopes. https://arxiv.org/abs/math/9704217

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