Simion’s Type B Associahedron is a Pulling Triangulation of the Legendre Polytope

Richard Ehrenborg; Gábor Hetyei; Margaret Readdy

doi:10.1007/s00454-018-9973-4

Simion’s Type B Associahedron is a Pulling Triangulation of the Legendre Polytope

Richard Ehrenborg, Gábor Hetyei, Margaret Readdy

Mathematics

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

5 Scopus citations

Abstract

We show that the Simion type B associahedron is combinatorially equivalent to a pulling triangulation of the type A root polytope known as the Legendre polytope. Furthermore, we show that every pulling triangulation of the boundary of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the boundary of the Legendre polytope given by Cho. Finally, we extend Cho’s cyclic group action to the triangulation in such a way that it corresponds to rotating centrally symmetric triangulations of a regular (2 n+ 2) -gon.

Original language	English
Pages (from-to)	98-114
Number of pages	17
Journal	Discrete and Computational Geometry
Volume	60
Issue number	1
DOIs	https://doi.org/10.1007/s00454-018-9973-4
State	Published - Jul 1 2018

Bibliographical note

Funding Information:
Acknowledgements The authors thank the Princeton University Mathematics Department where this research was initiated. The first author was partially funded by the National Security Agency Grant H98230-13-1-028. This work was partially supported by grants from the Simons Foundation (# 429370 to Richard Ehrenborg, # 245153 and # 514648 to Gábor Hetyei, # 206001 and # 422467 to Margaret Readdy). The authors also thank the three anonymous referees for their comments.

Publisher Copyright:
© 2018, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

Bott–Taubes polytope
Compressed polytopes
Cyclohedron
Flag complex
Stasheff polytope
Type A root polytope

ASJC Scopus subject areas

Theoretical Computer Science
Geometry and Topology
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1007/s00454-018-9973-4

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title = "Simion{\textquoteright}s Type B Associahedron is a Pulling Triangulation of the Legendre Polytope",

abstract = "We show that the Simion type B associahedron is combinatorially equivalent to a pulling triangulation of the type A root polytope known as the Legendre polytope. Furthermore, we show that every pulling triangulation of the boundary of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the boundary of the Legendre polytope given by Cho. Finally, we extend Cho{\textquoteright}s cyclic group action to the triangulation in such a way that it corresponds to rotating centrally symmetric triangulations of a regular (2 n+ 2) -gon.",

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note = "Funding Information: Acknowledgements The authors thank the Princeton University Mathematics Department where this research was initiated. The first author was partially funded by the National Security Agency Grant H98230-13-1-028. This work was partially supported by grants from the Simons Foundation (# 429370 to Richard Ehrenborg, # 245153 and # 514648 to G{\'a}bor Hetyei, # 206001 and # 422467 to Margaret Readdy). The authors also thank the three anonymous referees for their comments. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media, LLC, part of Springer Nature.",

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AU - Readdy, Margaret

N1 - Funding Information: Acknowledgements The authors thank the Princeton University Mathematics Department where this research was initiated. The first author was partially funded by the National Security Agency Grant H98230-13-1-028. This work was partially supported by grants from the Simons Foundation (# 429370 to Richard Ehrenborg, # 245153 and # 514648 to Gábor Hetyei, # 206001 and # 422467 to Margaret Readdy). The authors also thank the three anonymous referees for their comments. Publisher Copyright: © 2018, Springer Science+Business Media, LLC, part of Springer Nature.

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KW - Cyclohedron

KW - Flag complex

KW - Stasheff polytope

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Simion’s Type B Associahedron is a Pulling Triangulation of the Legendre Polytope

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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