A. Nixon

activity

20102023

most citedAnchored boundary conditions for locally isostatic networks

19 citations · 76 across the 28 of their papers we have counts for

collaborators

38 papers

math.CO2023

Rigidity of symmetric linearly constrained frameworks in the plane

Anthony Nixon, Bernd Schulze, Joseph Wall

A bar-joint framework $(G, p)$ is the combination of a finite simple graph $G = (V, E)$ and a placement $p : V \to R^{d}$ . The framework is rigid if the only edge-length pr…

math.CO2023★ 1 cited

On the uniqueness of collections of pennies and marbles

Sean Dewar, Georg Grasegger, Kaie Kubjas +2

In this note we study the uniqueness problem for collections of pennies and marbles. More generally, consider a collection of unit $d$ -spheres that may touch but not overlap. Given…

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.CO2022★ 3 cited

Computing maximum likelihood thresholds using graph rigidity

Daniel Irving Bernstein, Sean Dewar, Steven J. Gortler +3

The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding…

math.CO2022★ 1 cited

Rigidity of symmetric frameworks on the cylinder

Anthony Nixon, Bernd Schulze, Joseph Wall

A bar-joint framework $(G, p)$ is the combination of a finite simple graph $G = (V, E)$ and a placement $p : V \to R^{d}$ . The framework is rigid if the only edge-length pr…

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.MG2022

Universal Rigidity of Ladders on the line

Bryan Chen, Robert Connelly, Steven J. Gortler +2

In "Universal rigidity on the line, point orde" it is shown, answering a question of Jordán and Nguyen, that universal rigidity of a generic bar-joint framework in R^1 depends on m…

math.CO2022★ 1 cited

Uniquely realisable graphs in analytic normed planes

Sean Dewar, John Hewetson, Anthony Nixon

A bar-joint framework $(G, p)$ in the Euclidean space $E^{d}$ is globally rigid if it is the unique realisation, up to rigid congruences, of $G$ in $E^{d}$ with the ed…

math.CO2022★ 1 cited

Quotient graphs of symmetrically rigid frameworks

Sean Dewar, Georg Grasegger, Eleftherios Kastis +1

A natural problem in combinatorial rigidity theory concerns the determination of the rigidity or flexibility of bar-joint frameworks in $R^{d}$ that admit some non-trivial s…

math.CO2021

Coincident-point rigidity in normed planes

Sean Dewar, John Hewetson, Anthony Nixon

A bar-joint framework $(G, p)$ is the combination of a graph $G$ and a map $p$ assigning positions, in some space, to the vertices of $G$ . The framework is rigid if every edge-lengt…

math.MG2021★ 4 cited

Generalised rigid body motions in non-Euclidean planes with applications to global rigidity

Sean Dewar, Anthony Nixon

A bar-joint framework $(G, p)$ in a (non-Euclidean) real normed plane $X$ is the combination of a finite, simple graph $G$ and a placement $p$ of the vertices in $X$ . A framework $(…

math.CO2021★ 2 cited

Maximum likelihood thresholds via graph rigidity

Daniel Irving Bernstein, Sean Dewar, Steven J. Gortler +3

The maximum likelihood threshold (MLT) of a graph $G$ is the minimum number of samples to almost surely guarantee existence of the maximum likelihood estimate in the corresponding…

math.CO2021

Universal rigidity on the line, point order

Bryan Chen, Robert Connelly, Anthony Nixon +1

We show that universal rigidity of a generic bar and joint framework (G,p) in the line depends on more than the ordering of the vertices. In particular, we construct examples of on…

math.CO2020

An improved bound for the rigidity of linearly constrained frameworks

Bill Jackson, Anthony Nixon, Shin-Ichi Tanigawa

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.MG2020★ 7 cited

Which graphs are rigid in $ℓ_{p}^{d}$ ?

Sean Dewar, Derek Kitson, Anthony Nixon

We present three results which support the conjecture that a graph is minimally rigid in $d$ -dimensional $ℓ_{p}$ -space, where $p \in (1, \infty)$ and $p \neq = 2$ , if and only if it is…

math.CO2020

Flexible circuits in the $d$ -dimensional rigidity matroid

Georg Grasegger, Hakan Guler, Bill Jackson +1

A bar-joint framework $(G, p)$ in $R^{d}$ is rigid if the only edge-length preserving continuous motions of the vertices arise from isometries of $R^{d}$ . It is known…

math.CO2019★ 5 cited

Global rigidity of 2-dimensional linearly constrained frameworks

Hakan Guler, Bill Jackson, Anthony Nixon

A linearly constrained framework in $R^{d}$ is a point configuration together with a system of constraints which fixes the distances between some pairs of points and additio…

math.CO2019

Pairing symmetries for Euclidean and spherical frameworks

Katie Clinch, Anthony Nixon, Bernd Schulze +1

In this paper we consider the effect of symmetry on the rigidity of bar-joint frameworks, spherical frameworks and point-hyperplane frameworks in $R^{d}$ . In particular we s…

math.MG2018

Rigidity of symmetric frameworks in normed spaces

Derek Kitson, Anthony Nixon, Bernd Schulze

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-ty…

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.MG2017

Double-distance frameworks and mixed sparsity graphs

Anthony Nixon, Stephen Power

A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal an…

math.CO2017★ 2 cited

Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

Yaser Eftekhari, Bill Jackson, Anthony Nixon +3

A one-to-one correspondence between the infinitesimal motions of bar-joint frameworks in $R^{d}$ and those in $S^{d}$ is a classical observation by Pogorelov, and fur…

math.CO2016

Global rigidity of generic frameworks on the cylinder

Bill Jackson, Anthony Nixon

We show that a generic framework $(G, p)$ on the cylinder is globally rigid if and only if $G$ is a complete graph on at most four vertices or $G$ is both redundantly rigid and $2$ -…

math.CO2016

Rigid cylindrical frameworks with two coincident points

Bill Jackson, Viktoria Kaszanitzky, Anthony Nixon

We develop a rigidity theory for frameworks in $R^{3}$ which have two coincident points but are otherwise generic and only infinitesimal motions which are tangential to a fa…

Rigidity of symmetric linearly constrained frameworks in the plane

On the uniqueness of collections of pennies and marbles

Identifiability of Points and Rigidity of Hypergraphs under Algebraic Constraints

Computing maximum likelihood thresholds using graph rigidity

Rigidity of symmetric frameworks on the cylinder

Global Rigidity of Line Constrained Frameworks

Universal Rigidity of Ladders on the line

Uniquely realisable graphs in analytic normed planes

Quotient graphs of symmetrically rigid frameworks

Coincident-point rigidity in normed planes

Generalised rigid body motions in non-Euclidean planes with applications to global rigidity

Maximum likelihood thresholds via graph rigidity

Universal rigidity on the line, point order

An improved bound for the rigidity of linearly constrained frameworks

Which graphs are rigid in ℓpd​?

Flexible circuits in the d-dimensional rigidity matroid

Global rigidity of 2-dimensional linearly constrained frameworks

Pairing symmetries for Euclidean and spherical frameworks

Rigidity of symmetric frameworks in normed spaces

Rigidity of linearly-constrained frameworks

Double-distance frameworks and mixed sparsity graphs

Point-hyperplane frameworks, slider joints, and rigidity preserving transformations

Global rigidity of generic frameworks on the cylinder

Rigid cylindrical frameworks with two coincident points

Which graphs are rigid in $ℓ_{p}^{d}$ ?

Flexible circuits in the $d$ -dimensional rigidity matroid