Rigidity of partially symmetric structures

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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.