J. Cruickshank

activity

20092023

most citedRigidity of linearly-constrained frameworks

12 citations · 19 across the 13 of their papers we have counts for

collaborators

18 papers

math.MG2023

Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints

James Cruickshank, Fatemeh Mohammadi, Anthony Nixon +1

The identifiability problem arises naturally in a number of contexts in mathematics and computer science. Specific instances include local or global rigidity of graphs and unique c…

math.CO2023★ 1 cited

Rigidity of Symmetric Simplicial Complexes and the Lower Bound Theorem

James Cruickshank, Bill Jackson, Shinichi Tanigawa

We show that, if $Γ$ is a point group of $R^{k + 1}$ of order two for some $k \geq 2$ and $S$ is a $k$ -pseudomanifold which has a free automorphism of order two, the…

math.CO2022★ 1 cited

Global Rigidity of Line Constrained Frameworks

James Cruickshank, Fatemeh Mohammadi, Harshit J Motwani +2

We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $R^{d}$ . In our setting we allow multiple ver…

math.CO2022★ 3 cited

Global Rigidity of Triangulated Manifolds

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

We prove that if $G$ is the graph of a connected triangulated $(d - 1)$ -manifold, for $d \geq 3$ , then $G$ is generically globally rigid in $R^{d}$ if and only if it is $(d + 1)$ -…

math.CO2021

Braced triangulations and rigidity

James Cruickshank, Eleftherios Kastis, Derek Kitson +1

We consider the problem of finding an inductive construction, based on vertex splitting, of triangulated spheres with a fixed number of additional edges (braces). We show that for…

math.CO2020

Symmetric contact systems of segments, pseudotriangulations and inductive constructions for corresponding surface graphs

James Cruickshank, Bernd Schulze

We characterise the quotient surface graphs arising from symmetric contact systems of line segments in the plane and also from symmetric pointed pseudotriangulations in the case wh…

math.CO2020

Vertex Splitting, Coincident Realisations and Global Rigidity of Braced Triangulations

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

We give a short proof of a result of Jordan and Tanigawa that a 4-connected graph which has a spanning planar triangulation as a proper subgraph is generically globally rigid in R^…

math.CO2019

Topological inductive constructions for tight surface graphs

James Cruickshank, Derek Kitson, Stephen C. Power +1

We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $(2, 2)$ -tight surface graphs in the case of the spher…

math.RT2019

Weil representations via abstract data and Heisenberg groups: a comparison

James Cruickshank, Luis Gutiérrez Frez, Fernando Szechtman

Let $B$ be a ring, not necessarily commutative, having an involution $*$ and let $U_{2 m} (B)$ be the unitary group of rank $2 m$ associated to a hermitian or skew hermitian…

math.CO2018★ 12 cited

Rigidity of linearly-constrained frameworks

James Cruickshank, Hakan Guler, Bill Jackson +1

We consider the problem of characterising the generic rigidity of bar-joint frameworks in $R^{d}$ in which each vertex is constrained to lie in a given affine subspace. The…

math.GR2017

Generators and relations for the unitary group of a skew hermitian form over a local ring

James Cruickshank, Fernando Szechtman

Let $(S, *)$ be an involutive local ring and let $U (2 m, S)$ be the unitary group associated to a nondegenerate skew hermitian form defined on a free $S$ -module of rank $2 m$ . A presen…

math.RA2017

Hermitian and skew hermitian forms over local rings

James Cruickshank, Rachel Quinlan, Fernando Szechtman

We study the classification problem of possibly degenerate hermitian and skew hermitian bilinear forms over local rings where 2 is a unit.

math.RA2016★ 1 cited

Unitary groups and ramified extensions

J. Cruickshank, F. Szechtman

We classify all non-degenerate skew-hermitian forms defined over certain local rings, not necessarily commutative, and study some of the fundamental properties of the associated un…

math.CO2015★ 1 cited

The generic minimal rigidity of a partially triangulated torus

James Cruickshank, Derek Kitson, Stephen Power

A simple graph is $3$ -rigid if its generic bar-joint frameworks in $R^{3}$ are infinitesimally rigid. Necessary and sufficient conditions are obtained for the minimal $3$ -rigidity of…

math.FA2015

Positive Polynomials on Riesz Spaces

James Cruickshank, John Loane, Raymond A. Ryan

We prove some properties of positive polynomial mappings between Riesz spaces, using finite difference calculus. We establish the polynomial analogue of the classical result that p…

math.CO2015

The generic rigidity of triangulated spheres with blocks and holes

James Cruickshank, Derek Kitson, Stephen Power

A simple graph G=(V,E) is 3-rigid if its generic bar-joint frameworks in R3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of…

math.MG2013

On Spaces of Infinitesimal Motions and Henneberg Extensions

James Cruickshank

We investigate certain spaces of infinitesimal motions arising naturally in the rigidity theory of bar and joint frameworks. We prove some structure theorems for these spaces and a…

math.GT2009

Series Parallel Linkages

James Cruickshank, Jonathan McLaughlin

We study spaces of realisations of linkages (weighted graphs) whose underlying graph is a series parallel graph. In particular, we describe an algorithm for determining whether or…