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Constructing isostatic frameworks for the ℓ1and ℓ-plane

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Constructing isostatic frameworks for the ℓ1and ℓ-plane. / Clinch, Katie; Kitson, Derek.
In: The Electronic Journal of Combinatorics , Vol. 27, No. 2, P2.49, 12.06.2020.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Clinch, K & Kitson, D 2020, 'Constructing isostatic frameworks for the ℓ1and ℓ-plane', The Electronic Journal of Combinatorics , vol. 27, no. 2, P2.49. https://doi.org/10.37236/8196

APA

Clinch, K., & Kitson, D. (2020). Constructing isostatic frameworks for the ℓ1and ℓ-plane. The Electronic Journal of Combinatorics , 27(2), Article P2.49. https://doi.org/10.37236/8196

Vancouver

Clinch K, Kitson D. Constructing isostatic frameworks for the ℓ1and ℓ-plane. The Electronic Journal of Combinatorics . 2020 Jun 12;27(2):P2.49. doi: 10.37236/8196

Author

Clinch, Katie ; Kitson, Derek. / Constructing isostatic frameworks for the ℓ1and ℓ-plane. In: The Electronic Journal of Combinatorics . 2020 ; Vol. 27, No. 2.

Bibtex

@article{1e2070fc493b4da3bdeefdb9963a3f37,
title = "Constructing isostatic frameworks for the ℓ1and ℓ∞-plane",
abstract = "We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G=(V,E) has a partition into two spanning trees T1 and T2 then there is a map p:V→R2, p(v)=(p1(v),p2(v)), such that |pi(u)−pi(v)|⩾|p3−i(u)−p3−i(v)| for every edge uv in Ti(i=1,2). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the ℓ1 or ℓ∞-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.",
author = "Katie Clinch and Derek Kitson",
year = "2020",
month = jun,
day = "12",
doi = "10.37236/8196",
language = "English",
volume = "27",
journal = "The Electronic Journal of Combinatorics ",
issn = "1077-8926",
publisher = "Electronic Journal of Combinatorics",
number = "2",

}

RIS

TY - JOUR

T1 - Constructing isostatic frameworks for the ℓ1and ℓ∞-plane

AU - Clinch, Katie

AU - Kitson, Derek

PY - 2020/6/12

Y1 - 2020/6/12

N2 - We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G=(V,E) has a partition into two spanning trees T1 and T2 then there is a map p:V→R2, p(v)=(p1(v),p2(v)), such that |pi(u)−pi(v)|⩾|p3−i(u)−p3−i(v)| for every edge uv in Ti(i=1,2). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the ℓ1 or ℓ∞-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.

AB - We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G=(V,E) has a partition into two spanning trees T1 and T2 then there is a map p:V→R2, p(v)=(p1(v),p2(v)), such that |pi(u)−pi(v)|⩾|p3−i(u)−p3−i(v)| for every edge uv in Ti(i=1,2). As a consequence, we solve an open problem on the realisability of minimally rigid bar-joint frameworks in the ℓ1 or ℓ∞-plane. We also show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.

U2 - 10.37236/8196

DO - 10.37236/8196

M3 - Journal article

VL - 27

JO - The Electronic Journal of Combinatorics

JF - The Electronic Journal of Combinatorics

SN - 1077-8926

IS - 2

M1 - P2.49

ER -