Browsing Department of Mathematics and Computer Studies by Author "Kitson, Derek"

Now showing items 1-5 of 5

    • Constructing isostatic frameworks for the l1 and l infinity plane (Pre-published) 

      Clinch, Katie; Kitson, Derek (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 ...

    • Graph rigidity for unitarily invariant matrix norms (Pre-published) 

      Kitson, Derek; Levene, Rupert H (Elsevier, 2020-11-15)
      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 (Pre-published) 

      Kitson, Derek; Kastis, Eleftherios; McCarthy, John E (Elsevier, 2021-05-15)
      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 ...

    • Symmetric frameworks in normed spaces 

      Kitson, Derek; Nixon, Anthony; Schulze, Bernd (Elsevier, 2020-12-15)
      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 ...

    • Which graphs are rigid in lpd? 

      Dewar, Sean; Kitson, Derek; Nixon, Anthony (Springer, 2021-03-13)
      We present three results which support the conjecture that a graph is minimally rigid in d-dimensional ℓp-space, where p∈(1,∞) and p≠2, if and only if it is (d, d)-tight. Firstly, we introduce a graph bracing operation ...