Now showing items 1-5 of 5
Symmetric frameworks in normed spaces
We develop a combinatorial rigidity theory for symmetric bar-joint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwell-type sparsity counts are identified for a ...
Graph rigidity for unitarily invariant matrix norms
A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant matrix norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks ...
Symbol functions for symmetric frameworks
We prove a variant of the well-known result that intertwiners for the bilateral shift on ℓ2(Z) are unitarily equivalent to multiplication operators on L2(T). This enables us to unify and extend fundamental aspects of ...
Constructing isostatic frameworks for the l1 and l infinity plane
(Electronic Journal of Combinatorics, 2020-06-12)
We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G = (V,E) has a partition into two spanning trees T1 and T2 then there is a map p : V → R2, p(v) = (p(v)1,p(v)2), such that ...
The stability space of the derived category of holomorphic triples and further investigations
In this thesis we give a complete description of the Bridgeland stability space for the bounded derived category of holomorphic triples over a smooth projective curve of genus one as a connected, four dimensional complex ...