Rigidity of partially symmetric structures

条形连接框架是欧几里得空间中图形和实现的结合。如果唯一保持顶点连续运动的边长来自空间的等距，则框架是刚性的。一般来说，刚性可以很好地理解为一种纯粹的组合性质。然而，在大多数实际应用中，存在一些特殊的几何形状。最常见的特殊几何之一是对称或部分对称的存在。利用代数、几何和组合学的技术，该项目将寻求提供对部分对称框架何时是刚性的组合理解。

A bar-joint framework is the combination of a graph and a realisation in Euclidean space. The framework is rigid if the only edge-length preserving continuous motions of the vertices arise from isometries of the space. Generically, rigidity is well understood as a purely combinatorial property. However in most practical applications some particular geometry is present. One of the most common special geometry is the presence of symmetry or partial symmetry. Using techniques from algebra, geometry and combinatorics the project will seek to provide a combinatorial understanding of when a partially symmetric framework is rigid.