On Subdivision Posets of Cyclic Polytopes

Paul H. Edelman, Jörg Rambau, Victor S 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 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 languageEnglish (US)
Pages (from-to)85-101
Number of pages17
JournalEuropean Journal of Combinatorics
Volume21
Issue number1
DOIs
StatePublished - 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.

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