Publications

Peer-reviewed publications

2024

1. Maximum likelihood thresholds via graph rigidity. with D.I. Bernstein, S.J. Gortler, A. Nixon, M. Sitharam, L. Theran, Annals of Applied Probability (accepted). https://arxiv.org/abs/2108.02185

2. Computing maximum likelihood thresholds using graph rigidity. with D.I. Bernstein, S.J. Gortler, A. Nixon, M. Sitharam, L. Theran. Algebraic Statistics (accepted). https://arxiv.org/abs/2210.11081

3. Quotient graphs of symmetrically rigid frameworks. with G. Grasegger, E. Kastis, A. Nixon. Documenta Mathematica 29:3, 561-595. https://doi.org/10.4171/dm/958 

4. How many contacts can exist between oriented squares of various sizes? Discrete Mathematics 347:4, 113879. https://doi.org/10.1016/j.disc.2024.113879

2023

5. Coincident-point rigidity in normed planes. with J. Hewetson, A. Nixon. Ars Mathematica Contemporanea 24:1, #P1.10. https://doi.org/10.26493/1855-3974.2826.3dc

6. Graph rigidity properties of Ramanujan graphs. with S.M. Cioabă, G. Grasegger, X. Gu. The Electronic Journal of Combinatorics 30:3, #P3.12. https://doi.org/10.37236/11324

7. Classifying the globally rigid edge-transitive graphs and distance-regular graphs in the plane. Journal of Graph Theory 103:2, 175–185. https://doi.org/10.1002/jgt.22913

8. Flexing infinite frameworks with applications to braced Penrose tilings. with J. Legerský. Discrete Applied Mathematics 324, 1–17. https://doi.org/10.1016/j.dam.2022.09.002

2022

9. Infinitesimal rigidity and prestress stability for frameworks in normed spaces. Discrete Applied Mathematics 322, 425–438. https://doi.org/10.1016/j.dam.2022.09.001

10. Generalised rigid body motions in non-Euclidean planes with applications to global rigidity. with A. Nixon. Journal of Mathematical Analysis and Applications 514:1, 126259. https://doi.org/10.1016/j.jmaa.2022.126259

11. Homothetic packings of centrally symmetric convex bodies. Geometriae Dedicata 216, 11. https://doi.org/10.1007/s10711-022-00675-w

12. Flexible placements of graphs with rotational symmetry. with G. Grasegger, J. Legerský. 2nd IMA Conference on Mathematics of Robotics, 89–97. https://doi.org/10.1007/978-3-030-91352-6_9

13. Which graphs are rigid in Lpd? with D. Kitson, A. Nixon. Journal of Global Optimization 83, 49–71. https://doi.org/10.1007/s10898-021-01008-z

2021

14. Flexible placements of periodic graphs in the plane. Discrete and Computational Geometry 66, 1286–1329. https://doi.org/10.1007/s00454-021-00328-x

15. Spectral conditions for graph rigidity in the Euclidean plane. with S.M. Cioabă, X. Gu. Discrete Mathematics 344:10, 112527. https://doi.org/10.1016/j.disc.2021.112527

16. Equivalence of continuous, local and infinitesimal rigidity in normed spaces. Discrete and Computational Geometry 65, 655–679. https://doi.org/10.1007/s00454-019-00135-5

2020

17. Computing animations of linkages with rotational symmetry (media exposition). with G. Grasegger, J. Legerský. 36th International Symposium on Computational Geometry (SoCG 2020). https://doi.org/10.4230/LIPIcs.SoCG.2020.77

18. Infinitesimal rigidity in normed planes. SIAM Journal on Discrete Mathematics 34:2, 1205–1231. https://doi.org/10.1137/19M1284051

Data sets

2024

1. Non-planar graphs with various apex properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671129

2. Non-planar apex graphs with different independence properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671321

3. Non-planar (3,6)-sparse graphs with various apex properties. with G. Grasegger, E. Kastis, A. Nixon, B. Servatius. Zenodo. https://doi.org/10.5281/zenodo.10671293

2023

4. Marble graphs with various rigidity properties. with G. Grasegger, K. Kubjas, F. Mohammadi, A. Nixon. Zenodo. https://doi.org/10.5281/zenodo.8114283

2022

5. Ramanujan graphs with degree 3, 4, 5, 6, or 7. with S.M. Cioabă, G. Grasegger, X. Gu. Zenodo. https://doi.org/10.5281/zenodo.6579837

6. Rigidity of 4-regular Ramanujan graphs. with S.M. Cioabă, G. Grasegger, X. Gu. Zenodo. https://doi.org/10.5281/zenodo.6579718

Submitted publications

1. Edge-length preserving embeddings of graphs between normed spaces. with E. Kastis, D. Kitson, W. Sims. https://arxiv.org/abs/2405.02189

2. Angular constraints on planar frameworks. with  G. Grasegger, A. Nixon, Z. Rosen, W. Sims, M. Sitharam, D. Urizar. https://arxiv.org/abs/2403.16145

3. Extremal decompositions of tropical varieties and relations with rigidity theory. with  F. Babaee, J. Maxwell. http://arxiv.org/abs/2403.00655

4. Rigidity of nearly planar classes of graphs. with  G. Grasegger, E. Kastis, A. Nixon, B. Servatius. https://arxiv.org/abs/2402.17499

5. Rigid frameworks with dilation constraints. with  A. Nixon, A. Sainsbury. https://arxiv.org/abs/2402.14093

6. The number of realisations of a rigid graph in Euclidean and spherical geometries. with G. Grasegger. http://arxiv.org/abs/2309.16416

7. On the uniqueness of collections of pennies and marbles. with G. Grasegger, K. Kubjas, F. Mohammadi, A. Nixon. http://arxiv.org/abs/2307.03525

8. Rigid graphs in cylindrical normed spaces. with D. Kitson. http://arxiv.org/abs/2305.08421 

9. Identifying contact graphs of sphere packings with generic radii. https://arxiv.org/abs/2302.12588

10. Uniquely realisable graphs in analytic normed planes. with J. Hewetson, A. Nixon. https://arxiv.org/abs/2206.07426