Geodesic
Abstract 3-Rigidity and Bivariate $C_2^1$-Splines I: Whiteley's Maximality Conjecture
Discrete analysis (2022) Cet article a éte moissonné depuis la source Scholastica

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A conjecture of Graver from 1991 states that the generic $3$-dimensional rigidity matroid is the unique maximal abstract $3$-rigidity matroid with respect to the weak order on matroids. Based on a close similarity between the generic $d$-dimensional rigidity matroid and the generic $C_{d-2}^{d-1}$-cofactor matroid from approximation theory, Whiteley made an analogous conjecture in 1996 that the generic $C_{d-2}^{d-1}$-cofactor matroid is the unique maximal abstract $d$-rigidity matroid for all $d\geq 2$. We verify the case $d=3$ of Whiteley's conjecture in this paper. A key step in our proof is to verify a second conjecture of Whiteley that the `double V-replacement operation' preserves independence in the generic $C_2^1$-cofactor matroid.
Publié le : 
@article{DAS_2022_a17,
     author = {Katie Clinch and Bill Jackson and Shin-ichi Tanigawa},
     title = {Abstract {3-Rigidity} and {Bivariate} $C_2^1${-Splines} {I:} {Whiteley's} {Maximality} {Conjecture}},
     journal = {Discrete analysis},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2022_a17/}
}
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Katie Clinch; Bill Jackson; Shin-ichi Tanigawa. Abstract 3-Rigidity and Bivariate $C_2^1$-Splines I: Whiteley's Maximality Conjecture. Discrete analysis (2022). http://geodesic.mathdoc.fr/item/DAS_2022_a17/