The complex of non-crossing diagonals of a polygon

Benjamin Braun; Richard Ehrenborg

doi:10.1016/j.jcta.2010.03.003

The complex of non-crossing diagonals of a polygon

Benjamin Braun, Richard Ehrenborg

Mathematics

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

Abstract

Given a convex n-gon P in R{double-struck}2 with vertices in general position, it is well known that the simplicial complex θ(P) with vertex set given by diagonals in P and facets given by triangulations of P is the boundary complex of a polytope of dimension n-3. We prove that for any non-convex polygonal region P with n vertices and h+1 boundary components, θ(P) is a ball of dimension n+3h-4. We also provide a new proof that θ(P) is a sphere when P is convex with vertices in general position.

Original language	English
Pages (from-to)	642-649
Number of pages	8
Journal	Journal of Combinatorial Theory. Series A
Volume	117
Issue number	6
DOIs	https://doi.org/10.1016/j.jcta.2010.03.003
State	Published - Aug 2010

Bibliographical note

Funding Information:
E-mail addresses: [email protected] (B. Braun), [email protected] (R. Ehrenborg). URLs: http://www.ms.uky.edu/~braun (B. Braun), http://www.ms.uky.edu/~jrge (R. Ehrenborg). 1 Partially supported by National Science Foundation grant DMS-0758321. 2 Partially supported by National Security Agency grant H98230-06-1-0072.

Funding

E-mail addresses: [email protected] (B. Braun), [email protected] (R. Ehrenborg). URLs: http://www.ms.uky.edu/~braun (B. Braun), http://www.ms.uky.edu/~jrge (R. Ehrenborg). 1 Partially supported by National Science Foundation grant DMS-0758321. 2 Partially supported by National Security Agency grant H98230-06-1-0072.

Funders	Funder number
National Science Foundation (NSF)	DMS-0758321
Directorate for Mathematical and Physical Sciences	0758321
National Security Agency	H98230-06-1-0072

Keywords

Associahedra
Discrete Morse theory
Non-convex polygon
Simplicial complex

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Access to Document

10.1016/j.jcta.2010.03.003

Cite this

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title = "The complex of non-crossing diagonals of a polygon",

abstract = "Given a convex n-gon P in R{double-struck}2 with vertices in general position, it is well known that the simplicial complex θ(P) with vertex set given by diagonals in P and facets given by triangulations of P is the boundary complex of a polytope of dimension n-3. We prove that for any non-convex polygonal region P with n vertices and h+1 boundary components, θ(P) is a ball of dimension n+3h-4. We also provide a new proof that θ(P) is a sphere when P is convex with vertices in general position.",

keywords = "Associahedra, Discrete Morse theory, Non-convex polygon, Simplicial complex",

author = "Benjamin Braun and Richard Ehrenborg",

note = "Funding Information: E-mail addresses: [email protected] (B. Braun), [email protected] (R. Ehrenborg). URLs: http://www.ms.uky.edu/~braun (B. Braun), http://www.ms.uky.edu/~jrge (R. Ehrenborg). 1 Partially supported by National Science Foundation grant DMS-0758321. 2 Partially supported by National Security Agency grant H98230-06-1-0072.",

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KW - Discrete Morse theory

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KW - Simplicial complex

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The complex of non-crossing diagonals of a polygon

Abstract

Bibliographical note

Funding

Keywords

ASJC Scopus subject areas

Access to Document

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