Dr.
Georg Grasegger
Research Scientist
Symbolic Computation
Contact
Email: Georg.Grasegger(at)oeaw.ac.at
Telephone: +43 732 2468 5270
https://orcid.org/0000-0001-7421-8115
Research interests
- Rigidity Theory
- Symbolic Computation
- Algebraic Geometry
- Algebraic Differential Equations
Publications
Journal Publication (20)
- Grasegger, Georg; Legerský, Jan (2024) Flexibility and rigidity of frameworks consisting of triangles and parallelograms. Computational Geometry, Bd. 120, S. 102055.
- Grasegger, Georg; El Hilany, Boulos; Lubbes, Niels (2024, online: 2023) Coupler curves of moving graphs and counting realizations of rigid graphs. Mathematics of Computation, Bd. 93, S. 459-504.
- Cioabă, Sebastian M.; Dewar, Sean; Grasegger, Georg; Gu, Xiaofeng (2023) Graph Rigidity Properties of Ramanujan Graphs. Electronic Journal of Combinatorics, Bd. 30 (3), S. P3.12.
- Grasegger, Georg (2023) Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs. Examples and Counterexamples, Bd. 3, S. 100106.
- Grasegger, Georg; Legerský, Jan (2022, online: 2021) Bracing frameworks consisting of parallelograms. The Art of Discrete and Applied Mathematics, Bd. 5 (2), S. P2.03:1-21.
- Grasegger, Georg; Guler, Hakan; Jackson, Bill; Nixon, Anthony (2022, online: 2021) Flexible circuits in the d-dimensional rigidity matroid. Journal of Graph Theory, Bd. 100 (2), S. 315-330.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2022) Zero-sum cycles in flexible polyhedra. Bulletin of the London Mathematical Society, Bd. 54 (1), S. 112-125.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2021) On the existence of paradoxical motions of generically rigid graphs on the sphere. SIAM Journal on Discrete Mathematics, Bd. 35 (1), S. 325-361.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2021) Combinatorics of Bricard's octahedra. Comptes Rendus. Mathématique, Bd. 359 (1), S. 7-38.
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2020) On the Classification of Motions of Paradoxically Movable Graphs. Journal of Computational Geometry, Bd. 11 (1), S. 548-575.
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2020, online: 2019) Graphs with Flexible Labelings allowing Injective Realizations. Discrete Mathematics, Bd. 343 (6), S. 1-14.
- Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias (2020, online: 2018) Lower bounds on the number of realizations of rigid graphs. Experimental Mathematics, Bd. 29 (2), S. 125-136.
- Gallet, Matteo; Grasegger, Georg; Schicho, Josef (2020) Counting realizations of Laman graphs on the sphere. Electronic Journal of Combinatorics, Bd. 27 (2), S. P2.5 (1-18).
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2019, online: 2018) Graphs with Flexible Labelings. Discrete & Computational Geometry, Bd. 62 (2), S. 461-480.
- Vo, Thieu N.; Grasegger, Georg; Winkler, Franz (2018) Computation of all rational solutions of first-order algebraic ODEs. Advances in Applied Mathematics, Bd. 98, S. 1-24.
- Vo, N. Thieu; Grasegger, Georg; Winkler, Franz (2018, online: 2017) Deciding the existence of rational general solutions for first-order algebraic ODEs. Journal of Symbolic Computation, Bd. 87, S. 127-139.
- Grasegger, Georg; Lastra, Alberto; Sendra, J. Rafael; Winkler, Franz (2018, online: 2017) Rational General Solutions of Systems of First-Order Partial Differential Equations. Journal of Computational and Applied Mathematics (331), S. 88-103.
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels et al. [..] (2018) The number of realizations of a Laman graph. SIAM Journal on Applied Algebra and Geometry, Bd. 2 (1), S. 94-125.
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels et al. [..] (2017) Computing the number of realizations of a Laman graph. Electronic Notes in Discrete Mathematics, Bd. 61, S. 207-213.
- Grasegger, Georg; Lastra, Alberto; Sendra, J. Rafael; Winkler, Franz (2016) A solution method for autonomous first-order algebraic partial differential equations. Journal of Computational and Applied Mathematics, Bd. 300, S. 119--133.
Conference Contribution: Publication in Proceedings (9)
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2022, online: 2021) Zero-Sum Cycles in Flexible Non-triangular Polyhedra., 2nd IMA Conference on Mathematics of Robotics (IMA Conference on Mathematics of Robotics) In Reihe: Springer Proceedings in Advanced Robotics, hrsg. v. Holderbaum W., Selig J.M.: Springer, Cham, S. 137-143.
- Dewar, Sean; Grasegger, Georg; Legerský, Jan (2022, online: 2021) Flexible Placements of Graphs with Rotational Symmetry., 2nd IMA Conference on Mathematics of Robotics (IMA Conference on Mathematics of Robotics) In Reihe: Springer Proceedings in Advanced Robotics, hrsg. v. Holderbaum W., Selig J.M.: Springer, Cham, S. 89-97.
- Grasegger, Georg; Legerský, Jan (2020) FlexRiLoG—A SageMath Package for Motions of Graphs. In: Bigatti, A. and Carette, J. and Davenport, J. and Joswig, M. and de Wolff, T. (Hrsg.), Mathematical Software – ICMS 2020 (ICMS 2020) In Reihe: Lecture Notes in Computer Science, S. 442-450.
- Dewar, Sean; Grasegger, Georg; Legerský, Jan (2020) Computing Animations of Linkages with Rotational Symmetry. In: Informatik, Schloss Dagstuhl--Leibniz-Zentrum für (Hrsg.), 36th International Symposium on Computational Geometry (SoCG 2020) In Reihe: Leibniz International Proceedings in Informatics (LIPIcs).
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2019) Animated Motions of Exceptional Flexible Instances of Generically Rigid Graphs., Bridges Linz 2019 Conference Proceedings (Bridges 2019): Tessellations Publishing, S. 255–262.
- Grasegger, Georg (2018) Realizations and Constructions of Minimally Rigid Graphs., Bridges Stockholm 2018 Conference Proceedings (Bridges 2018): Tessellations Publishing, S. 239-242.
- Kimeswenger, Barbara; Grasegger, Georg; Reichenberger, Sandra (2018) Constructing Linkages for Drawing Curves., Bridges Stockholm 2018 Conference Proceedings (Bridges 2018): Tessellations Publishing, S. 613-616.
- Grasegger, Georg; Vo, N. Thieu (2017) An Algebraic-Geometric Method for Computing Zolotarev Polynomials. In: Burr, Michael (Hrsg.), Proceedings of the 2017 ACM (International Symposium on Symbolic and Algebraic Computation (ISSAC)) In Reihe: ISSAC '17; Kaiserslautern: ACM, S. 173-180.
- Grasegger, Georg; Vo, N. Thieu; Winkler, Franz (2016) A decision algorithm for rational general solutions of first-order algebraic ODEs. In: Rioja, Universidad de La (Hrsg.), XV Encuentro de Álgebra computacional y aplicaciones (Encuentros de Álgebra Computacional y Aplicaciones, EACA); Logroño, S. 101-104.
Research Report (28)
- Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios; Nixon, Anthony; Servatius, Brigitte (online: 2024) Rigidity of nearly planar classes of graphs. Bericht-Nr. arXiv:2402.17499;.
- Dewar, Sean; Grasegger, Georg (2023) The number of realisations of a rigid graph in Euclidean and spherical geometries. Bericht-Nr. 2309.16416;.
- Dewar, Sean; Grasegger, Georg (online: 2023) The number of realisations of a rigid graph in Euclidean and spherical geometries. Bericht-Nr. arXiv.2309.16416;.
- Gallet, Matteo; Grasegger, Georg; Lubbes, Niels; Schicho, Josef (2023) Calligraphs and sphere realizations. Bericht-Nr. arXiv:2308.15305;.
- Dewar, Sean; Grasegger, Georg; Kubjas, Kaie; Mohammadi, Fatemeh; Nixon, Anthony (2023) On the uniqueness of collections of pennies and marbles. Bericht-Nr. arXiv:2307.03525;.
- Grasegger, Georg; Legerský, Jan (2023) Flexibility and rigidity of frameworks consisting of triangles and parallelograms. Bericht-Nr. arXiv:2305.01570;.
- Grasegger, Georg (2022) Minimal counterexamples to Hendrickson's conjecture on globally rigid graphs. Bericht-Nr. arXiv:2212.11818;.
- Cioabă, Sebastian M.; Dewar, Sean; Grasegger, Georg; Gu, Xiaofeng (online: 2022) Graph rigidity properties of Ramanujan graphs.
- Grasegger, Georg; El Hilany, Boulos; Lubbes, Niels (online: 2022) Coupler curves of moving graphs and counting realizations of rigid graphs. Bericht-Nr. 2205.02612;.
- Dewar, Sean; Grasegger, Georg; Kastis, Eleftherios; Nixon, Anthony (online: 2022) Quotient graphs of symmetrically rigid frameworks. Bericht-Nr. 2202.09165;.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2021) Zero-sum cycles in flexible non-triangular polyhedra. Bericht-Nr. arXiv:2108.08744;.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2020) Zero-sum cycles in flexible polyhedra. Bericht-Nr. arXiv:2009.14041;.
- Grasegger, Georg; Legerský, Jan (2020) Bracing frameworks consisting of parallelograms. Bericht-Nr. arXiv:2008.11521;.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2020) Combinatorics of Bricard's octahedra. Bericht-Nr. arXiv:2004.01236;.
- Grasegger, Georg; Legerský, Jan (2020) FlexRiLoG -- A SageMath Package for Motions of Graphs. Bericht-Nr. arXiv:2003.12029;.
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2020) On the Classification of Motions of Paradoxically Movable Graphs. Bericht-Nr. arXiv:2003.11416;.
- Dewar, Sean; Grasegger, Georg; Legerský, Jan (2020) Flexible placements of graphs with rotational symmetry. Bericht-Nr. arXiv:2003.09328;.
- Grasegger, Georg; Guler, Hakan; Jackson, Bill; Nixon, Anthony (2020) Flexible circuits in the d-dimensional rigidity matroid. Bericht-Nr. arXiv:2003.06648;.
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2019) Classification of motions of the 3-connected Harary graph on 7 vertices. Bericht-Nr. 10.5281/zenodo.3561920; Zenodo:.
- Gallet, Matteo; Grasegger, Georg; Legerský, Jan; Schicho, Josef (2019) On the existence of paradoxical motions of generically rigid graphs on the sphere. Bericht-Nr. arXiv:1908.00467;.
- Gallet, Matteo; Grasegger, Georg; Schicho, Josef (2019) Counting realizations of Laman graphs on the sphere. Bericht-Nr. arXiv:1903.01145;.
- Grasegger, Georg; Legerský, Jan; Schicho, Josef (2018) Graphs with Flexible Labelings allowing Injective Realizations. Bericht-Nr. arXiv:1811.06709;.
- Grasegger, Georg; Koutschan, Christoph; Tsigaridas, Elias (2017) Lower bounds on the number of realizations of rigid graphs. Bericht-Nr. 2017-35; RICAM: Linz.
- Grasegger, Georg; Legersky, Jan; Schicho, Josef (2017) Graphs with Flexible Labelings. Bericht-Nr. arXiv:1708.05298;.
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels et al. [..] (2017) The number of realizations of a Laman graph. Bericht-Nr. 2017-03; RICAM: Linz.
- Grasegger, Georg (2016) An Algebraic-Geometric Method for Computing Zolotarev Polynomials — Additional Information. Bericht-Nr. 16-07; RISC, Johannes Kepler University Linz:.
- Grasegger, Georg; Vo, N. Thieu (2016) An Algebraic-Geometric Method for Computing Zolotarev Polynomials. Bericht-Nr. 16-02; RISC, Johannes Kepler University Linz:.
- Grasegger, Georg; Vo, N. Thieu; Winkler, Franz (2015) Statistical Investigation of First-Order Algebraic ODEs and their Rational General Solutions. Bericht-Nr. 15-19; RISC, Johannes Kepler University Linz:.
Other Publication (1)
Research data collection (6)
- Dewar, Sean; Grasegger, Georg; Kubjas, Kaie; Mohammadi, Fatemeh; Nixon, Anthony (2023) Marble graphs with various rigidity properties.
- Grasegger, Georg (2022) Dataset of globally rigid graphs.
- Grasegger, Georg (2022) Dataset of redundantly rigid graphs.
- Cioabă, Sebastian M.; Dewar, Sean; Grasegger, Georg; Gu, Xiaofeng (2022) Rigidity of 4-regular Ramanujan graphs.
- Cioabă, Sebastian M.; Dewar, Sean; Grasegger, Georg; Gu, Xiaofeng (2022) Ramanujan graphs with degree 3, 4, 5, 6, or 7.
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels et al. [..] (online: 2018) The number of realizations of all Laman graphs with at most 12 vertices. Bericht-Nr. 10.5281/zenodo.1245517;.
Software (5)
- Grasegger, Georg (2022) RigiComp - A Mathematica package for computational rigidity of graphs.
- Gallett, Matteo; Grasegger, Georg; Schicho, Josef (2022) Software for counting realizations of minimally rigid graphs on the sphere.
- Grasegger, Georg; El Hilany, Boulos; Lubbes, Niels (2022) Calligraphs and counting realizations of minimally rigid graphs.
- Grasegger, Georg; Legerský, Jan (2019) FlexRiLoG - SageMath package for Flexible and Rigid Labelings of Graphs. Bericht-Nr. 10.5281/zenodo.3078758;.
- Capco, Jose; Gallet, Matteo; Grasegger, Georg; Koutschan, Christoph; Lubbes, Niels et al. [..] (online: 2018) An algorithm for computing the number of realizations of a Laman graph. Bericht-Nr. 10.5281/zenodo.1245506;.