Triangle-free triangulations

Ron M. Adin; Marcelo Firer; Yuval Roichman

doi:10.1016/j.aam.2009.11.001

Triangle-free triangulations

Ron M. Adin, Marcelo Firer, Yuval Roichman

Department of Mathematics

Universidade Estadual de Campinas

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

4 Scopus citations

Abstract

The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group over(C, ̃)_n acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on over(C, ̃)_n. Lattice properties of this order are then applied to compute the diameter.

Original language	English
Pages (from-to)	77-95
Number of pages	19
Journal	Advances in Applied Mathematics
Volume	45
Issue number	1
DOIs	https://doi.org/10.1016/j.aam.2009.11.001
State	Published - Jul 2010

Keywords

Coxeter groups
Flips
Group actions
Hasse diagrams
Schreier graphs
Triangulations
Weak order

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10.1016/j.aam.2009.11.001

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abstract = "The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group over(C,{\~ })n acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on over(C,{\~ })n. Lattice properties of this order are then applied to compute the diameter.",

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AB - The flip operation on colored inner-triangle-free triangulations of a convex polygon is studied. It is shown that the affine Weyl group over(C, ̃)n acts transitively on these triangulations by colored flips, and that the resulting colored flip graph is closely related to a lower interval in the weak order on over(C, ̃)n. Lattice properties of this order are then applied to compute the diameter.

KW - Coxeter groups

KW - Flips

KW - Group actions

KW - Hasse diagrams

KW - Schreier graphs

KW - Triangulations

KW - Weak order

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JO - Advances in Applied Mathematics

JF - Advances in Applied Mathematics

IS - 1

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Triangle-free triangulations

Abstract

Keywords

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