RIGIDITY OF FRAMEWORKS ON EXPANDING SPHERES

被引：4

作者：

Nixon, Anthony ^{[1
]}

Schulze, Bernd ^{[1
]}

Tanigawa, Shin-ichi ^{[2
]}

Whiteley, Walter ^{[3
]}

机构：

[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

[2] Univ Tokyo, Dept Math Informat, Bunkyo Ku, 7-3-1 Hongo, Tokyo 1138656, Japan

[3] York Univ, Dept Math & Stat, 4700 Keele St, Toronto, ON M3J 1P3, Canada

来源：

SIAM JOURNAL ON DISCRETE MATHEMATICS | 2018年 / 32卷 / 04期

基金：

加拿大自然科学与工程研究理事会;

关键词：

rigidity of graphs; bar-joint frameworks; expanding sphere; rigidity matroids; count matroids; symmetry; SYMMETRY-FORCED RIGIDITY; GRAPHS;

D O I：

10.1137/17M1116088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A rigidity theory is developed for bar-joint frameworks in Rd+1 whose vertices are constrained to lie on concentric d-spheres with independently variable radii. In particular, combinatorial characterizations are established for the rigidity of generic frameworks for d = 1 with an arbitrary number of independently variable radii, and for d = 2 with at most two variable radii. This includes a characterization of the rigidity or flexibility of uniformly expanding spherical frameworks in R-3. Due to the equivalence of the generic rigidity between Euclidean space and spherical space, these results interpolate between rigidity in one and two dimensions and to some extent between rigidity in two and three dimensions. Symmetry-adapted counts for the detection of symmetry-induced continuous flexibility in frameworks on spheres with variable radii are also provided.

引用

页码：2591 / 2611

页数：21