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Geometric Rigidity

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  1. 2025
  2. Published

    On the uniqueness of collections of pennies and marbles

    Dewar, S., Grasegger, G., Kubjas, K., Mohammadi, F. & Nixon, A., 30/06/2025, In: Examples and Counterexamples. 7, 100181.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  3. Published

    Rigidity of Symmetric Frameworks on the Cylinder

    Nixon, A., Schulze, B. & Wall, J., 30/04/2025, In: Discrete and Computational Geometry. 73, p. 629-673 45 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  4. Forthcoming

    Singly-periodic pointed pseudotriangulations have an expansive motion

    Esson, J., Kastis, E. & Schulze, B., 23/04/2025, (Accepted/In press) Proceeding of the 3rd IMA Conference on Mathematics of Robotics. Springer

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Conference contribution/Paper › peer-review

  5. Published

    Single-cell 3D genome reconstruction in the haploid setting using rigidity theory

    Dewar, S., Grasegger, G., Kubjas, K., Mohammadi, F. & Nixon, A., 1/04/2025, In: Journal of Mathematical Biology. 90, 4, 45.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  6. Published

    Rigid frameworks with dilation constraints

    Dewar, S., Nixon, A. & Sainsbury, A., 28/02/2025, In: Discrete Mathematics. 348, 2, 114304.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  7. Published

    Rigidity of symmetric linearly constrained frameworks in the plane

    Nixon, A., Schulze, B. & Wall, J., 30/01/2025, In: Discrete Applied Mathematics. 361, p. 370-388 19 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  8. Published

    The infinitesimal rigidity of symmetric bar-joint frameworks with non-free joints

    La Porta, A., 2025, Lancaster University. 256 p.

    Research output: Thesis › Doctoral Thesis

  9. 2024
  10. Published

    Stable cuts, NAC-colourings and flexible realisations of graphs

    Clinch, K., Garamvölgyi, D., Haslegrave, J., Huynh, T., Nixon, A. & Legerský, J., 20/12/2024, Arxiv, 18 p.

    Research output: Working paper › Preprint

  11. E-pub ahead of print

    Geometry of tropical extensions of hyperfields

    Maxwell, J. & Smith, B., 26/11/2024, (E-pub ahead of print) In: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 42 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  12. Published

    On complete classes of valuated matroids

    Husic, E., Loho, G., Smith, B. & Vegh, L. A., 18/11/2024, In: TheoretiCS. 3, 10755.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  13. Published

    Uniquely realisable graphs in analytic normed planes

    Dewar, S., Hewetson, J. & Nixon, A., 30/09/2024, In: International Mathematics Research Notices. 2024, 17, p. 12269-12302 33 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  14. Forthcoming

    Root polytopes, tropical types, and toric edge ideals

    Almousa, A., Dochtermann, A. & Smith, B., 29/09/2024, (Accepted/In press) In: Algebraic Combinatorics.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  15. Forthcoming

    Universal rigidity of ladders on the line

    Chen, B., Connelly, R., Gortler, S., Nixon, A. & Theran, L., 30/06/2024, (Accepted/In press) In: Studia Scientiarum Mathematicarum Hungarica: Combinatorics, Geometry and Topology.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  16. Published

    Maximum likelihood thresholds via graph rigidity

    Bernstein, D., Dewar, S., Gortler, S., Nixon, A., Sitharam, M. & Theran, L., 13/06/2024, In: Annals of Applied Probability. 34, 3, p. 3288-3319 32 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  17. Published

    Quotient graphs of symmetrically rigid frameworks

    Dewar, S., Grasegger, G., Kastis, E. & Nixon, A., 8/05/2024, In: Documenta Mathematica. 29, 3, p. 561-595 35 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  18. Published

    The parabolic algebra revisited

    Kastis, E. & Power, S., 1/03/2024, In: Israel Journal of Mathematics. 259, 2, p. 559-587 29 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  19. Published

    Rigidity of frameworks on spheres

    Hewetson, J. & Nixon, A., 23/02/2024, Graphs and Combinatorial Optimization: from Theory to Applications. CTW 2023. Brieden, A., Pickl, S. & Siegle, M. (eds.). Cham: Springer, p. 41-52 12 p. (AIRO Springer Series; vol. 13).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

  20. Published

    Global Rigidity of Line Constrained Frameworks

    Cruickshank, J., Mohammadi, F., Motwani, H., Nixon, A. & Tanigawa, S., 6/02/2024, In: SIAM Journal on Discrete Mathematics. 38, 1

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  21. Published

    Equilibrium stresses and rigidity for infinite tensegrities and frameworks

    Power, S., 1/01/2024, In: Journal of Mathematical Analysis and Applications. 529, 1, 127655.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  22. Published

    Symmetric Frameworks on Surfaces

    Wall, J., 2024, Lancaster University. 187 p.

    Research output: Thesis › Doctoral Thesis

  23. 2023
  24. Published

    Computing maximum likelihood thresholds using graph rigidity

    Bernstein, D., Dewar, S., Gortler, S., Nixon, A., Sitharam, M. & Theran, L., 31/12/2023, In: Algebraic Statistics. 14, 2, p. 287-305 19 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  25. Published

    Face Posets of Tropical Polyhedra and Monomial Ideals

    Loho, G. & Smith, B., 20/10/2023, In: The Electronic Journal of Combinatorics. 30, 4, 57 p., P4.11.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  26. Published

    Coincident-point rigidity in normed planes

    Dewar, S., Hewetson, J. & Nixon, A., 7/09/2023, In: Ars Mathematica Contemporanea. 24, 1, 17 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  27. Published

    Corrigendum to: Flexible circuits in the d-dimensional rigidity matroid (Journal of Graph Theory, (2022), 100, 2, (315-330), 10.1002/jgt.22780)

    Grasegger, G., Guler, H., Jackson, B. & Nixon, A., 30/06/2023, In: Journal of Graph Theory. 103, 2, p. 307-308 2 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  28. Published

    Convergent Hahn Series and Tropical Geometry of Higher Rank

    Joswig, M. & Smith, B., 30/04/2023, In: Journal of the London Mathematical Society. 107, 4, p. 1450-1481 32 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  29. Published

    Recursive combinatorial constructions and rigidity of frameworks

    Hewetson, J., 2023, Lancaster University. 192 p.

    Research output: Thesis › Doctoral Thesis

  30. 2022
  31. Published

    Linear zero mode spectra for quasicrystals

    Power, S., 15/12/2022, In: Journal of Mathematical Analysis and Applications. 516, 2, 19 p., 126534.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  32. Published

    Topological inductive constructions for tight surface graphs

    Cruickshank, J., Kitson, D., Power, S. & Shakir, Q., 12/10/2022, In: Graphs and Combinatorics. 38, 31 p., 169.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  33. Published

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

    Dewar, S. & Nixon, A., 1/10/2022, In: Journal of Mathematical Analysis and Applications. 514, 1, 31 p., 126259.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  34. Published

    Flexible circuits in the d-dimensional rigidity matroid

    Grasegger, G., Guler, H., Jackson, B. & Nixon, A., 30/06/2022, In: Journal of Graph Theory. 100, 2, p. 315-360 16 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  35. Published

    The Rigidity of Infinite Graphs II

    Kitson, D. & Power, S., 30/06/2022, In: Graphs and Combinatorics. 38, 3, 83.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  36. Published

    Surveys in Combinatorics 2022

    Nixon, A. & Prendiville, S., 31/05/2022, Cambridge University Press. 259 p. (London Mathematical Society Lecture Note Series; vol. 481)

    Research output: Book/Report/Proceedings › Book

  37. Published

    Which graphs are rigid in l_p^d?

    Dewar, S., Kitson, D. & Nixon, A., 31/05/2022, In: Journal of Global Optimization. 83, 1, p. 49-71 23 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  38. 2021
  39. Published

    Rigidity through a Projective Lens

    Nixon, A., Schulze, B. & Whiteley, W., 15/12/2021, In: Applied Science. 11, 24, 105 p., e11946.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  40. Published

    The first-order flexibility of a crystallographic framework

    Kastis, E. & Power, S., 1/12/2021, In: Journal of Mathematical Analysis and Applications. 504, 1, 16 p., 125404.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  41. Published

    Global rigidity of 2D linearly constrained frameworks

    Guler, H., Jackson, B. & Nixon, A., 30/11/2021, In: International Mathematics Research Notices. 2021, 22, p. 16811-16858 48 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  42. E-pub ahead of print

    Crystal flex bases and the RUM spectrum

    Badri, G., Kitson, D. & Power, S., 24/11/2021, (E-pub ahead of print) In: Proceedings of the Edinburgh Mathematical Society. 64, 4, p. 735-761 27 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  43. Published

    Parallelogram Frameworks and Flexible Quasicrystals

    Power, S., 31/08/2021, In: Mathematical Proceedings of the Royal Irish Academy. 121A, 1, p. 9-31 23 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  44. Published

    Symbol functions for symmetric frameworks

    Kastis, E., Kitson, D. & McCarthy, J., 15/05/2021, In: Journal of Mathematical Analysis and Applications. 497, 2, 24 p., 124895.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  45. Published

    An improved bound for the rigidity of linearly constrained frameworks

    Jackson, B., Nixon, A. & Tanigawa, S.-I., 4/05/2021, In: SIAM Journal on Discrete Mathematics. 35, 2, p. 928–933 6 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  46. Published

    Equivalence of Continuous, Local and Infinitesimal Rigidity in Normed Spaces

    Dewar, S., 30/04/2021, In: Discrete and Computational Geometry. 65, p. 655–679 25 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  47. Published

    Rado's criterion over squares and higher powers

    Chow, S., Lindqvist, S. & Prendiville, S., 16/02/2021, In: Journal of the European Mathematical Society. 23, 6, p. 1925-1997 73 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  48. 2020
  49. Published

    Rigidity of symmetric frameworks in normed spaces

    Kitson, D., Nixon, A. & Schulze, B., 15/12/2020, In: Linear Algebra and its Applications. 607, p. 231-285 49 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  50. Published

    Graph rigidity for unitarily invariant matrix norms

    Kitson, D. & Levene, R. H., 15/11/2020, In: Journal of Mathematical Analysis and Applications. 491, 2, 30 p., 124353.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  51. Published

    Assur decompositions of direction-length frameworks

    Nixon, A., 9/11/2020, Graphs and Combinatorial Optimization : from Theory to Applications : CTW2020 Proceedings. Gentile, C., Stecca, G. & Ventura, P. (eds.). Cham: Springer, p. 131-143 12 p. (AIRO Springer).

    Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter (peer-reviewed) › peer-review

  52. Published

    Non-Euclidean braced grids

    Power, S., 31/10/2020, In: Mathematical Proceedings of the Royal Irish Academy. 120A, 2, p. 43-57 15 p., PRIA.2020.120.06.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  53. Published

    Pairing symmetries for Euclidean and spherical frameworks

    Clinch, K., Nixon, A., Schulze, B. & Whiteley, W., 1/09/2020, In: Discrete and Computational Geometry. 64, p. 483–518 36 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  54. Published

    Constructing isostatic frameworks for the ℓ1and ℓ∞-plane

    Clinch, K. & Kitson, D., 12/06/2020, In: The Electronic Journal of Combinatorics . 27, 2, 21 p., P2.49.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  55. Published

    Rigidity of linearly constrained frameworks

    Cruickshank, J., Guler, H., Jackson, B. & Nixon, A. K., 1/06/2020, In: International Mathematics Research Notices. 2020, 12, p. 3824-3840 17 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

  56. Published

    Isotopy classes for 3-periodic net embeddings

    Power, S., Baburin, I. & Proserpio, D., 1/05/2020, In: Acta Crystallographica Section A: Foundations and Advances. 76, 3, p. 275-301 27 p.

    Research output: Contribution to Journal/Magazine › Journal article › peer-review

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