Symbolic-Numeric Techniques for Genus Computation and Parametrization [DK9]
Project Lead
Project Duration
01/10/2014 - 30/06/2022Project URL
Go to Website
Partners
The Austrian Science Fund (FWF)
Publications
2021
[Grasegger]
On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere
M. Gallet, G. Grasegger, J. Legerský, J. Schicho
SIAM Journal on Discrete Mathematics 35(1), pp. 325-361. 2021. ISSN 0895-4801. [doi]@article{RISC6290,
author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere}},
language = {english},
journal = {SIAM Journal on Discrete Mathematics},
volume = {35},
number = {1},
pages = {325--361},
isbn_issn = {ISSN 0895-4801},
year = {2021},
refereed = {yes},
length = {37},
url = {https://doi.org/10.1137/19M1289467}
}
author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{On the Existence of Paradoxical Motions of Generically Rigid Graphs on the Sphere}},
language = {english},
journal = {SIAM Journal on Discrete Mathematics},
volume = {35},
number = {1},
pages = {325--361},
isbn_issn = {ISSN 0895-4801},
year = {2021},
refereed = {yes},
length = {37},
url = {https://doi.org/10.1137/19M1289467}
}
2020
[Grasegger]
Graphs with Flexible Labelings allowing Injective Realizations
G. Grasegger, J. Legerský, J. Schicho
Discrete Mathematics 343(6), pp. Art. 111713-. 2020. ISSN 0012-365X. [doi]@article{RISC6012,
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{Graphs with Flexible Labelings allowing Injective Realizations}},
language = {english},
journal = {Discrete Mathematics},
volume = {343},
number = {6},
pages = {Art. 111713--},
isbn_issn = {ISSN 0012-365X},
year = {2020},
refereed = {yes},
length = {14},
url = {https://doi.org/10.1016/j.disc.2019.111713}
}
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{Graphs with Flexible Labelings allowing Injective Realizations}},
language = {english},
journal = {Discrete Mathematics},
volume = {343},
number = {6},
pages = {Art. 111713--},
isbn_issn = {ISSN 0012-365X},
year = {2020},
refereed = {yes},
length = {14},
url = {https://doi.org/10.1016/j.disc.2019.111713}
}
[Grasegger]
FlexRiLoG - A SageMath Package for Motions of Graphs
G. Grasegger, J. Legerský
In: Mathematical Software – ICMS 2020, Bigatti A., Carette J., Davenport J., Joswig M., de Wolff T. (ed.), Proceedings of ICMS 2020, Lecture Notes in Computer Science 12097, pp. 442-450. 2020. Springer, Cham, ISBN 978-3-030-52199-8. [doi]@inproceedings{RISC6182,
author = {G. Grasegger and J. Legerský},
title = {{FlexRiLoG - A SageMath Package for Motions of Graphs}},
booktitle = {{ Mathematical Software – ICMS 2020}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {12097},
pages = {442--450},
publisher = {Springer, Cham},
isbn_issn = {ISBN 978-3-030-52199-8},
year = {2020},
editor = {Bigatti A. and Carette J. and Davenport J. and Joswig M. and de Wolff T.},
refereed = {no},
length = {9},
conferencename = {ICMS 2020},
url = {https://doi.org/10.1007/978-3-030-52200-1_44}
}
author = {G. Grasegger and J. Legerský},
title = {{FlexRiLoG - A SageMath Package for Motions of Graphs}},
booktitle = {{ Mathematical Software – ICMS 2020}},
language = {english},
series = {Lecture Notes in Computer Science},
volume = {12097},
pages = {442--450},
publisher = {Springer, Cham},
isbn_issn = {ISBN 978-3-030-52199-8},
year = {2020},
editor = {Bigatti A. and Carette J. and Davenport J. and Joswig M. and de Wolff T.},
refereed = {no},
length = {9},
conferencename = {ICMS 2020},
url = {https://doi.org/10.1007/978-3-030-52200-1_44}
}
[Grasegger]
Zero-sum cycles in flexible polyhedra
M. Gallet, G. Grasegger, J. Legerský, J. Schicho
arXiv. Technical report, 2020. [url]@techreport{RISC6211,
author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{Zero-sum cycles in flexible polyhedra}},
language = {english},
year = {2020},
institution = {arXiv},
length = {16},
url = {https://arxiv.org/abs/2009.14041}
}
author = {M. Gallet and G. Grasegger and J. Legerský and J. Schicho},
title = {{Zero-sum cycles in flexible polyhedra}},
language = {english},
year = {2020},
institution = {arXiv},
length = {16},
url = {https://arxiv.org/abs/2009.14041}
}
[Grasegger]
On the Classification of Motions of Paradoxically Movable Graphs
G. Grasegger, J. Legerský, J. Schicho
Journal of Computational Geometry 11(1), pp. 548-575. 2020. ISSN: 1920-180X. [doi]@article{RISC6239,
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{On the Classification of Motions of Paradoxically Movable Graphs}},
language = {english},
journal = {Journal of Computational Geometry},
volume = {11},
number = {1},
pages = {548--575},
isbn_issn = {ISSN: 1920-180X},
year = {2020},
refereed = {yes},
length = {27},
url = {https://doi.org/10.20382/jocg.v11i1a22}
}
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{On the Classification of Motions of Paradoxically Movable Graphs}},
language = {english},
journal = {Journal of Computational Geometry},
volume = {11},
number = {1},
pages = {548--575},
isbn_issn = {ISSN: 1920-180X},
year = {2020},
refereed = {yes},
length = {27},
url = {https://doi.org/10.20382/jocg.v11i1a22}
}
2019
[Grasegger]
Graphs with Flexible Labelings
G. Grasegger, J. Legerský, J. Schicho
Discrete & Computational Geometry 62(2), pp. 461-480. 2019. 1432-0444. arXiv:1708.05298. [doi]@article{RISC5803,
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{Graphs with Flexible Labelings}},
language = {english},
journal = {Discrete & Computational Geometry},
volume = {62},
number = {2},
pages = {461--480},
isbn_issn = {1432-0444},
year = {2019},
note = {arXiv:1708.05298},
refereed = {yes},
length = {20},
url = {https://doi.org/10.1007/s00454-018-0026-9}
}
author = {G. Grasegger and J. Legerský and J. Schicho},
title = {{Graphs with Flexible Labelings}},
language = {english},
journal = {Discrete & Computational Geometry},
volume = {62},
number = {2},
pages = {461--480},
isbn_issn = {1432-0444},
year = {2019},
note = {arXiv:1708.05298},
refereed = {yes},
length = {20},
url = {https://doi.org/10.1007/s00454-018-0026-9}
}
2018
[Koutschan]
The Number of Realizations of a Laman Graph
Jose Capco, Matteo Gallet, Georg Grasegger, Christoph Koutschan, Niels Lubbes, Josef Schicho
SIAM Journal on Applied Algebra and Geometry 2(1), pp. 94-125. 2018. 2470-6566. [doi]@article{RISC5700,
author = {Jose Capco and Matteo Gallet and Georg Grasegger and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{The Number of Realizations of a Laman Graph}},
language = {english},
journal = {SIAM Journal on Applied Algebra and Geometry},
volume = {2},
number = {1},
pages = {94--125},
isbn_issn = {2470-6566},
year = {2018},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1137/17M1118312}
}
author = {Jose Capco and Matteo Gallet and Georg Grasegger and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{The Number of Realizations of a Laman Graph}},
language = {english},
journal = {SIAM Journal on Applied Algebra and Geometry},
volume = {2},
number = {1},
pages = {94--125},
isbn_issn = {2470-6566},
year = {2018},
refereed = {yes},
length = {32},
url = {https://doi.org/10.1137/17M1118312}
}
2017
[Koutschan]
The number of realizations of a Laman graph
Jose Capco, Georg Grasegger, Matteo Gallet, Christoph Koutschan, Niels Lubbes, Josef Schicho
Research Institute for Symbolic Computation (RISC/JKU). Technical report, 2017. [url] [pdf]@techreport{RISC5418,
author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{The number of realizations of a Laman graph}},
language = {english},
abstract = {Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursion formula for the number of complex solutions of such systems. },
year = {2017},
institution = {Research Institute for Symbolic Computation (RISC/JKU)},
length = {42},
url = {http://www.koutschan.de/data/laman/}
}
author = {Jose Capco and Georg Grasegger and Matteo Gallet and Christoph Koutschan and Niels Lubbes and Josef Schicho},
title = {{The number of realizations of a Laman graph}},
language = {english},
abstract = {Laman graphs model planar frameworks that are rigid for a general choice of distances between the vertices. There are finitely many ways, up to isometries, to realize a Laman graph in the plane. Such realizations can be seen as solutions of systems of quadratic equations prescribing the distances between pairs of points. Using ideas from algebraic and tropical geometry, we provide a recursion formula for the number of complex solutions of such systems. },
year = {2017},
institution = {Research Institute for Symbolic Computation (RISC/JKU)},
length = {42},
url = {http://www.koutschan.de/data/laman/}
}
