Geodesic
Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization
Discrete analysis (2022) Cet article a éte moissonné depuis la source Scholastica

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We showed in the first paper of this series that the generic $C_2^1$-cofactor matroid is the unique maximal abstract $3$-rigidity matroid. In this paper we obtain a combinatorial characterization of independence in this matroid. This solves the cofactor counterpart of the combinatorial characterization problem for the rigidity of generic 3-dimensional bar-joint frameworks. We use our characterization to verify that the counterparts of conjectures of Dress (on the rank function) and Lovász and Yemini (which suggested a sufficient connectivity condition for rigidity) hold for this matroid.
Publié le : 
@article{DAS_2022_a16,
     author = {Katie Clinch and Bill Jackson and Shin-ichi Tanigawa},
     title = {Abstract {3-Rigidity} and {Bivariate} $C_2^1${-Splines} {II:} {Combinatorial} {Characterization}},
     journal = {Discrete analysis},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2022_a16/}
}
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JO  - Discrete analysis
PY  - 2022
UR  - http://geodesic.mathdoc.fr/item/DAS_2022_a16/
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%A Shin-ichi Tanigawa
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Katie Clinch; Bill Jackson; Shin-ichi Tanigawa. Abstract 3-Rigidity and Bivariate $C_2^1$-Splines II: Combinatorial Characterization. Discrete analysis (2022). http://geodesic.mathdoc.fr/item/DAS_2022_a16/