Layered circle packings

David Dennis; G. Brock Williams

doi:10.1155/IJMMS.2005.2429

Layered circle packings

David Dennis, G. Brock Williams

Mathematics and Statistics

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

2 Scopus citations

Abstract

Given a bounded sequence of integers {d₀, d₁, d₂,...}, 6 ≤ d_n ≤ M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree d_n. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {d_n}.

Original language	English
Pages (from-to)	2429-2440
Number of pages	12
Journal	International Journal of Mathematics and Mathematical Sciences
Volume	2005
Issue number	15
DOIs	https://doi.org/10.1155/IJMMS.2005.2429
State	Published - Sep 29 2005

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title = "Layered circle packings",

abstract = "Given a bounded sequence of integers {d0, d1, d2,...}, 6 ≤ dn ≤ M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {dn}.",

author = "David Dennis and Williams, {G. Brock}",

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AU - Williams, G. Brock

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N2 - Given a bounded sequence of integers {d0, d1, d2,...}, 6 ≤ dn ≤ M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {dn}.

AB - Given a bounded sequence of integers {d0, d1, d2,...}, 6 ≤ dn ≤ M, there is an associated abstract triangulation created by building up layers of vertices so that vertices on the nth layer have degree dn. This triangulation can be realized via a circle packing which fills either the Euclidean or the hyperbolic plane. We give necessary and sufficient conditions to determine the type of the packing given the defining sequence {dn}.

UR - http://www.scopus.com/inward/record.url?scp=29144464225&partnerID=8YFLogxK

U2 - 10.1155/IJMMS.2005.2429

DO - 10.1155/IJMMS.2005.2429

M3 - Article

AN - SCOPUS:29144464225

SN - 0161-1712

VL - 2005

SP - 2429

EP - 2440

JO - International Journal of Mathematics and Mathematical Sciences

JF - International Journal of Mathematics and Mathematical Sciences

IS - 15

ER -

Layered circle packings

Abstract

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