Realizing Simion's type B associahedron as a pulling triangulation of the Legendre polytope

Richard Ehrenborg; Gábor Hetyei; Margaret Readdy

Realizing Simion's type B associahedron as a pulling triangulation of the Legendre polytope

Richard Ehrenborg, Gábor Hetyei, Margaret Readdy

Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

We show that Simion's type B associahedron is combinatorially equivalent to a pulling triangulation of a type B root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the Legendre polytope given by Cho. 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 (2n + 2)-gon.

Original language	English
State	Published - 2006
Event	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 - London, United Kingdom Duration: Jul 9 2017 → Jul 13 2017

Conference

Conference	29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017
Country/Territory	United Kingdom
City	London
Period	7/9/17 → 7/13/17

Bibliographical note

Funding Information:
The first author was partially funded by the National Security Agency grant H98230-13-1-028. This work was partially supported by two grants from the Simons Foundation (#245153 to Gábor Hetyei and #206001 to Margaret Readdy). The authors thank the Princeton University Mathematics Department where this research was initiated, and two anonymous referees for many insightful comments.

Publisher Copyright:
© 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

Keywords

Associahedron
Root polytope
Type B

ASJC Scopus subject areas

Algebra and Number Theory

Cite this

@conference{48591d1e69fb4f44a22ce5c354951a2d,

title = "Realizing Simion's type B associahedron as a pulling triangulation of the Legendre polytope",

abstract = "We show that Simion's type B associahedron is combinatorially equivalent to a pulling triangulation of a type B root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the Legendre polytope given by Cho. 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 (2n + 2)-gon.",

keywords = "Associahedron, Root polytope, Type B",

author = "Richard Ehrenborg and G{\'a}bor Hetyei and Margaret Readdy",

note = "Funding Information: The first author was partially funded by the National Security Agency grant H98230-13-1-028. This work was partially supported by two grants from the Simons Foundation (#245153 to G{\'a}bor Hetyei and #206001 to Margaret Readdy). The authors thank the Princeton University Mathematics Department where this research was initiated, and two anonymous referees for many insightful comments. Publisher Copyright: {\textcopyright} 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.; 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017 ; Conference date: 09-07-2017 Through 13-07-2017",

year = "2006",

language = "English",

}

TY - CONF

T1 - Realizing Simion's type B associahedron as a pulling triangulation of the Legendre polytope

AU - Ehrenborg, Richard

AU - Hetyei, Gábor

AU - Readdy, Margaret

N1 - Funding Information: The first author was partially funded by the National Security Agency grant H98230-13-1-028. This work was partially supported by two grants from the Simons Foundation (#245153 to Gábor Hetyei and #206001 to Margaret Readdy). The authors thank the Princeton University Mathematics Department where this research was initiated, and two anonymous referees for many insightful comments. Publisher Copyright: © 29th international conference on Formal Power Series and Algebraic Combinatorics. All rights reserved.

PY - 2006

Y1 - 2006

N2 - We show that Simion's type B associahedron is combinatorially equivalent to a pulling triangulation of a type B root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the Legendre polytope given by Cho. 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 (2n + 2)-gon.

AB - We show that Simion's type B associahedron is combinatorially equivalent to a pulling triangulation of a type B root polytope called the Legendre polytope. Furthermore, we show that every pulling triangulation of the Legendre polytope yields a flag complex. Our triangulation refines a decomposition of the Legendre polytope given by Cho. 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 (2n + 2)-gon.

KW - Associahedron

KW - Root polytope

KW - Type B

UR - http://www.scopus.com/inward/record.url?scp=85091906118&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85091906118&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:85091906118

T2 - 29th international conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2017

Y2 - 9 July 2017 through 13 July 2017

ER -

Realizing Simion's type B associahedron as a pulling triangulation of the Legendre polytope

Abstract

Conference

Bibliographical note

Keywords

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this