On Subdivision Posets of Cyclic Polytopes

Paul H. Edelman; Jörg Rambau; Victor S Reiner

doi:10.1006/eujc.1999.0320

On Subdivision Posets of Cyclic Polytopes

Paul H. Edelman
, Jörg Rambau
, Victor S Reiner

School of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

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	https://doi.org/10.1006/eujc.1999.0320
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.

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10.1006/eujc.1999.0320

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title = "On Subdivision Posets of Cyclic Polytopes",

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.",

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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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AU - Edelman, Paul H.

AU - Rambau, Jörg

AU - Reiner, Victor S

N1 - 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.

PY - 2000/1

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N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0034420788

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EP - 101

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

IS - 1

ER -

On Subdivision Posets of Cyclic Polytopes

Abstract

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