# Doctoral Program “Computational Mathematics” [DK W1214]

### Project Lead

### Project Duration

01/10/2008 - 31/12/2022### Project URL

Go to Website## Partners

### The Austrian Science Fund (FWF)

## Publications

### 2024

[Qi]

### A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero

#### Jiayue Qi

Journal of Symbolic Computation 122(102253), pp. -. 2024. ISSN: 0747-7171. [doi]@

author = {Jiayue Qi},

title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {122},

number = {102253},

pages = {--},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

refereed = {yes},

length = {52},

url = {https://doi.org/10.1016/j.jsc.2023.102253}

}

**article**{RISC6774,author = {Jiayue Qi},

title = {{A tree-based algorithm for the integration of monomials in the Chow ring of the moduli space of stable marked curves of genus zero}},

language = {english},

journal = {Journal of Symbolic Computation},

volume = {122},

number = {102253},

pages = {--},

isbn_issn = {ISSN: 0747-7171},

year = {2024},

refereed = {yes},

length = {52},

url = {https://doi.org/10.1016/j.jsc.2023.102253}

}

### 2023

[Qi]

### Five Equivalent Representations of a Phylogenetic Tree

#### Jiayue Qi, Josef Schicho

Maple Transactions 3(3), pp. -. 2023. (ISSN) 2564-3029. [doi]@

author = {Jiayue Qi and Josef Schicho},

title = {{Five Equivalent Representations of a Phylogenetic Tree}},

language = {english},

journal = {Maple Transactions},

volume = {3},

number = {3},

pages = {--},

isbn_issn = {(ISSN) 2564-3029},

year = {2023},

refereed = {yes},

length = {15},

url = {https://doi.org/10.5206/mt.v3i3.16464}

}

**article**{RISC6777,author = {Jiayue Qi and Josef Schicho},

title = {{Five Equivalent Representations of a Phylogenetic Tree}},

language = {english},

journal = {Maple Transactions},

volume = {3},

number = {3},

pages = {--},

isbn_issn = {(ISSN) 2564-3029},

year = {2023},

refereed = {yes},

length = {15},

url = {https://doi.org/10.5206/mt.v3i3.16464}

}

[Qi]

### On the Chow ring of (the) moduli space of stable marked curves of genus zero

#### Jiayue Qi

Research Institute for Symbolic Computation, Johannes Kepler University Linz. PhD Thesis. 2023.@

author = {Jiayue Qi},

title = {{On the Chow ring of (the) moduli space of stable marked curves of genus zero}},

language = {English},

year = {2023},

translation = {0},

school = {Research Institute for Symbolic Computation, Johannes Kepler University Linz},

length = {127}

}

**phdthesis**{RISC6945,author = {Jiayue Qi},

title = {{On the Chow ring of (the) moduli space of stable marked curves of genus zero}},

language = {English},

year = {2023},

translation = {0},

school = {Research Institute for Symbolic Computation, Johannes Kepler University Linz},

length = {127}

}

### 2022

[Qi]

### An identity on multinomial coefficients

#### Jiayue Qi

ACM Communications in Computer Algebra 56(2), pp. 68-71. 2022. issn: 1932-2240. [doi]@

author = {Jiayue Qi},

title = {{An identity on multinomial coefficients}},

language = {english},

abstract = {We introduce an identity on multinomial coefficients, as well as the proof for it.},

journal = {ACM Communications in Computer Algebra},

volume = {56},

number = {2},

pages = {68--71},

isbn_issn = {issn: 1932-2240},

year = {2022},

refereed = {yes},

length = {4},

url = {https://doi.org/10.1145/3572867.3572878}

}

**article**{RISC6770,author = {Jiayue Qi},

title = {{An identity on multinomial coefficients}},

language = {english},

abstract = {We introduce an identity on multinomial coefficients, as well as the proof for it.},

journal = {ACM Communications in Computer Algebra},

volume = {56},

number = {2},

pages = {68--71},

isbn_issn = {issn: 1932-2240},

year = {2022},

refereed = {yes},

length = {4},

url = {https://doi.org/10.1145/3572867.3572878}

}

### 2021

[Qi]

### How to avoid collisions in 3D-realizations for moving graphs

#### Jiayue Qi

Mechanism and Machine Theory 162(104337), pp. -. 2021. ISSN 0094-114X. [doi]@

author = {Jiayue Qi},

title = {{How to avoid collisions in 3D-realizations for moving graphs}},

language = {english},

journal = {Mechanism and Machine Theory },

volume = {162},

number = {104337},

pages = {--},

isbn_issn = {ISSN 0094-114X},

year = {2021},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.mechmachtheory.2021.104337}

}

**article**{RISC6772,author = {Jiayue Qi},

title = {{How to avoid collisions in 3D-realizations for moving graphs}},

language = {english},

journal = {Mechanism and Machine Theory },

volume = {162},

number = {104337},

pages = {--},

isbn_issn = {ISSN 0094-114X},

year = {2021},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.mechmachtheory.2021.104337}

}

[Qi]

### A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves

#### Jiayue Qi

ACM Communications in Computer Algebra 54(3), pp. 91-94. 2021. issn: 1932-2240. [doi]@

author = {Jiayue Qi},

title = {{A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves}},

language = {english},

abstract = {We introduce an algorithm for computing the value of all monomials in the Chow group of zero cycles in the moduli space of stable curves.},

journal = {ACM Communications in Computer Algebra},

volume = {54},

number = {3},

pages = {91--94},

isbn_issn = {issn: 1932-2240},

year = {2021},

refereed = {yes},

length = {4},

url = {https://doi.org/10.1145/3457341.3457344}

}

**article**{RISC6780,author = {Jiayue Qi},

title = {{A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves}},

language = {english},

abstract = {We introduce an algorithm for computing the value of all monomials in the Chow group of zero cycles in the moduli space of stable curves.},

journal = {ACM Communications in Computer Algebra},

volume = {54},

number = {3},

pages = {91--94},

isbn_issn = {issn: 1932-2240},

year = {2021},

refereed = {yes},

length = {4},

url = {https://doi.org/10.1145/3457341.3457344}

}

[Qi]

### A tree-based algorithm on monomials in the Chow group of zero cycles in the moduli space of stable pointed curves of genus zero

#### Jiayue Qi

Doctoral Program “Computational Mathematics”. Technical report, January 2021. [url]@

author = {Jiayue Qi},

title = {{A tree-based algorithm on monomials in the Chow group of zero cycles in the moduli space of stable pointed curves of genus zero}},

language = {english},

year = {2021},

month = {January},

institution = {Doctoral Program “Computational Mathematics”},

length = {43},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2021-01-11qi/view}

}

**techreport**{RISC6785,author = {Jiayue Qi},

title = {{A tree-based algorithm on monomials in the Chow group of zero cycles in the moduli space of stable pointed curves of genus zero}},

language = {english},

year = {2021},

month = {January},

institution = {Doctoral Program “Computational Mathematics”},

length = {43},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2021-01-11qi/view}

}

### 2020

[Qi]

### Five Equivalent Ways to Describe a Phylogenetic Tree

#### Jiayue Qi, Josef Schicho

Doctoral Program “Computational Mathematics”. Technical report, December 2020. [url]@

author = {Jiayue Qi and Josef Schicho},

title = {{Five Equivalent Ways to Describe a Phylogenetic Tree}},

language = {english},

year = {2020},

month = {December},

institution = {Doctoral Program “Computational Mathematics”},

length = {20},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-11-30jiayue/view}

}

**techreport**{RISC6784,author = {Jiayue Qi and Josef Schicho},

title = {{Five Equivalent Ways to Describe a Phylogenetic Tree}},

language = {english},

year = {2020},

month = {December},

institution = {Doctoral Program “Computational Mathematics”},

length = {20},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-11-30jiayue/view}

}

[Qi]

### A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves

#### Jiayue Qi

Doctoral Program “Computational Mathematics”. Technical report, November 2020. [url]@

author = {Jiayue Qi},

title = {{A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves}},

language = {english},

year = {2020},

month = {November},

institution = {Doctoral Program “Computational Mathematics”},

keywords = {monomials in Chow ring, monomial value, tree representations, recursive algorithm on forest},

length = {5},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-09-18/view}

}

**techreport**{RISC6787,author = {Jiayue Qi},

title = {{A calculus for monomials in Chow group of zero cycles in the moduli space of stable curves}},

language = {english},

year = {2020},

month = {November},

institution = {Doctoral Program “Computational Mathematics”},

keywords = {monomials in Chow ring, monomial value, tree representations, recursive algorithm on forest},

length = {5},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-09-18/view}

}

[Qi]

### How fast can Dominator win in the Maker-Breaker domination game?

#### Jiayue Qi, Jovana Forcan

Doctoral Program “Computational Mathematics”. Technical report, October 2020. [url]@

author = {Jiayue Qi and Jovana Forcan},

title = {{How fast can Dominator win in the Maker-Breaker domination game?}},

language = {english},

year = {2020},

month = {October},

institution = {Doctoral Program “Computational Mathematics”},

keywords = {domination number, Maker–Braker domination number, positional game, grid, winning strategy},

length = {26},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-07-15/view}

}

**techreport**{RISC6789,author = {Jiayue Qi and Jovana Forcan},

title = {{How fast can Dominator win in the Maker-Breaker domination game?}},

language = {english},

year = {2020},

month = {October},

institution = {Doctoral Program “Computational Mathematics”},

keywords = {domination number, Maker–Braker domination number, positional game, grid, winning strategy},

length = {26},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2020-07-15/view}

}

### 2019

[Jimenez Pastor]

### A Computable Extension for Holonomic Functions: DD-Finite Functions

#### Jiménez-Pastor Antonio, Pillwein Veronika

Journal of Symbolic Computation 94, pp. 90-104. September-October 2019. ISSN 0747-7171. [doi]@

author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},

language = {english},

abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},

journal = {Journal of Symbolic Computation},

volume = {94},

pages = {90--104},

isbn_issn = {ISSN 0747-7171},

year = {2019},

month = {September-October},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.jsc.2018.07.002}

}

**article**{RISC5831,author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{A Computable Extension for Holonomic Functions: DD-Finite Functions}},

language = {english},

abstract = {Differentiably finite (D-finite) formal power series form a large class of useful functions for which a variety of symbolic algorithms exists. Among these methods are several closure properties that can be carried out automatically. We introduce a natural extension of these functions to a larger class of computable objects for which we prove closure properties. These are again algorithmic. This extension can be iterated constructively preserving the closure properties},

journal = {Journal of Symbolic Computation},

volume = {94},

pages = {90--104},

isbn_issn = {ISSN 0747-7171},

year = {2019},

month = {September-October},

refereed = {yes},

length = {15},

url = {https://doi.org/10.1016/j.jsc.2018.07.002}

}

[Qi]

### How to avoid collision of 3D-realization for moving graphs

#### Jiayue Qi

Doctoral Program “Computational Mathematics”. Technical report, December 2019. [url]@

author = {Jiayue Qi},

title = {{How to avoid collision of 3D-realization for moving graphs}},

language = {english},

year = {2019},

month = {December},

institution = {Doctoral Program “Computational Mathematics”},

length = {14},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2019-12-16/view}

}

**techreport**{RISC6791,author = {Jiayue Qi},

title = {{How to avoid collision of 3D-realization for moving graphs}},

language = {english},

year = {2019},

month = {December},

institution = {Doctoral Program “Computational Mathematics”},

length = {14},

url = {https://www.dk-compmath.jku.at/publications/dk-reports/2019-12-16/view}

}

### 2018

[Jimenez Pastor]

### Algorithmic Arithmetics with DD-Finite Functions

#### Jiménez-Pastor Antonio, Pillwein Veronika

In: Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation, Arreche Carlos (ed.), ISSAC '18 , pp. 231-237. 2018. ACM, New York, NY, USA, ISBN 978-1-4503-5550-6. [doi]@

author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{Algorithmic Arithmetics with DD-Finite Functions}},

booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '18},

pages = {231--237},

publisher = {ACM},

address = {New York, NY, USA},

isbn_issn = {ISBN 978-1-4503-5550-6},

year = {2018},

editor = {Arreche Carlos},

refereed = {yes},

keywords = {algorithms, closure properties, holonomic functions},

length = {7},

url = {http://doi.acm.org/10.1145/3208976.3209009}

}

**inproceedings**{RISC5730,author = {Jiménez-Pastor Antonio and Pillwein Veronika},

title = {{Algorithmic Arithmetics with DD-Finite Functions}},

booktitle = {{Proceedings of the 2018 ACM on International Symposium on Symbolic and Algebraic Computation}},

language = {english},

series = {ISSAC '18},

pages = {231--237},

publisher = {ACM},

address = {New York, NY, USA},

isbn_issn = {ISBN 978-1-4503-5550-6},

year = {2018},

editor = {Arreche Carlos},

refereed = {yes},

keywords = {algorithms, closure properties, holonomic functions},

length = {7},

url = {http://doi.acm.org/10.1145/3208976.3209009}

}

[Pillwein]

### Positivity of the Gillis-Reznick-Zeilberger rational function

#### V. Pillwein

Technical report no. 18-05 in RISC Report Series, Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, Austria. ISSN 2791-4267 (online). 2018. [pdf]@

author = {V. Pillwein},

title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},

language = {english},

number = {18-05},

year = {2018},

length = {12},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

**techreport**{RISC5612,author = {V. Pillwein},

title = {{Positivity of the Gillis-Reznick-Zeilberger rational function}},

language = {english},

number = {18-05},

year = {2018},

length = {12},

type = {RISC Report Series},

institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},

address = {Altenberger Straße 69, 4040 Linz, Austria},

issn = {2791-4267 (online)}

}

[Raab]

### Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations

#### J. Ablinger, A. Behring, J. Blümlein, A. De Freitas, E. Imamoglu, M. van Hoeij A. von Manteuffel, C.G. Raab, C.-S. Radu, C. Schneider

In: Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology), A. Hoang, C. Schneider (ed.)PoS (RADCOR2017) 069, pp. 1-13. 2018. ISSN 1824-8039. arXiv:1711.09742 [hep-ph]. [doi]@

author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2018},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://doi.org/10.22323/1.290.0069 }

}

**inproceedings**{RISC5350,author = {J. Ablinger and A. Behring and J. Blümlein and A. De Freitas and E. Imamoglu and M. van Hoeij A. von Manteuffel and C.G. Raab and C.-S. Radu and C. Schneider},

title = {{Iterative and Iterative-Noniterative Integral Solutions in 3-Loop Massive QCD Calculations}},

booktitle = {{Proc. of the 13th International Symposium on Radiative Corrections (Applications of Quantum Field Theory to Phenomenology)}},

language = {english},

volume = {PoS (RADCOR2017) 069},

pages = {1--13},

isbn_issn = {ISSN 1824-8039},

year = {2018},

note = {arXiv:1711.09742 [hep-ph]},

editor = {A. Hoang and C. Schneider},

refereed = {no},

length = {13},

url = {https://doi.org/10.22323/1.290.0069 }

}

[Schicho]

### On sets defining few ordinary circles

#### A. Lin, M. Makhul, H. N. Mojarrad, J. Schicho, K. Swanepoel, F. de Zeeuw

Discrete and Computational Geometry 59, pp. 59-87. 2018. 0179-5376.@

author = {A. Lin and M. Makhul and H. N. Mojarrad and J. Schicho and K. Swanepoel and F. de Zeeuw},

title = {{On sets defining few ordinary circles}},

language = {english},

journal = {Discrete and Computational Geometry},

volume = {59},

pages = {59--87},

isbn_issn = {0179-5376},

year = {2018},

refereed = {yes},

length = {29}

}

**article**{RISC5535,author = {A. Lin and M. Makhul and H. N. Mojarrad and J. Schicho and K. Swanepoel and F. de Zeeuw},

title = {{On sets defining few ordinary circles}},

language = {english},

journal = {Discrete and Computational Geometry},

volume = {59},

pages = {59--87},

isbn_issn = {0179-5376},

year = {2018},

refereed = {yes},

length = {29}

}

### 2017

[Buchberger]

### Gröbner Bases Computation by Triangularizing Macaulay Matrices

#### Bruno Buchberger

Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases) 75, pp. 1-9. 2017. Mathematical Society of Japan, 0.@

author = {Bruno Buchberger},

title = {{Gröbner Bases Computation by Triangularizing Macaulay Matrices}},

language = {english},

journal = {Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases)},

volume = {75},

pages = {1--9},

publisher = {Mathematical Society of Japan},

isbn_issn = {0},

year = {2017},

refereed = {no},

length = {9}

}

**article**{RISC5586,author = {Bruno Buchberger},

title = {{Gröbner Bases Computation by Triangularizing Macaulay Matrices}},

language = {english},

journal = {Advanced Studies in Pure Mathematics (The 50th Anniversary of Gröbner Bases)},

volume = {75},

pages = {1--9},

publisher = {Mathematical Society of Japan},

isbn_issn = {0},

year = {2017},

refereed = {no},

length = {9}

}

[Buchberger]

### Satisfiability Checking and Symbolic Computation

#### Abraham Erika , Abbott John , Becker Bernd , Bigatti Anna Maria , Brain Martin , Buchberger Bruno , Cimatti Alessandro , Davenport James , England Matthew , Fontaine Pascal , Forrest Stephen , Griggio Alberto , Kröning Daniel , Seiler Werner M. , Sturm

ACM Communications in Computer Algebra 50(4), pp. 145-147. 2017. 0.@

author = { Abraham Erika and Abbott John and Becker Bernd and Bigatti Anna Maria and Brain Martin and Buchberger Bruno and Cimatti Alessandro and Davenport James and England Matthew and Fontaine Pascal and Forrest Stephen and Griggio Alberto and Kröning Daniel and Seiler Werner M. and Sturm },

title = {{Satisfiability Checking and Symbolic Computation}},

language = {english},

journal = {ACM Communications in Computer Algebra},

volume = {50},

number = {4},

pages = {145--147},

isbn_issn = {0},

year = {2017},

refereed = {no},

length = {3}

}

**article**{RISC5587,author = { Abraham Erika and Abbott John and Becker Bernd and Bigatti Anna Maria and Brain Martin and Buchberger Bruno and Cimatti Alessandro and Davenport James and England Matthew and Fontaine Pascal and Forrest Stephen and Griggio Alberto and Kröning Daniel and Seiler Werner M. and Sturm },

title = {{Satisfiability Checking and Symbolic Computation}},

language = {english},

journal = {ACM Communications in Computer Algebra},

volume = {50},

number = {4},

pages = {145--147},

isbn_issn = {0},

year = {2017},

refereed = {no},

length = {3}

}

[Koutschan]

### Planar linkages following a prescribed motion

#### M. Gallet, C. Koutschan, Z. Li, G. Regensburger, J. Schicho, N. Villamizar

Math. Comp. 87, pp. 473-506. 2017. ISSN: 1088-6842. [url]@

author = {M. Gallet and C. Koutschan and Z. Li and G. Regensburger and J. Schicho and N. Villamizar},

title = {{Planar linkages following a prescribed motion}},

language = {english},

journal = {Math. Comp.},

volume = {87},

pages = {473--506},

isbn_issn = {ISSN: 1088-6842},

year = {2017},

refereed = {yes},

length = {34},

url = {http://www.ams.org/journals/mcom/2017-86-303/S0025-5718-2016-03120-8/}

}

**article**{RISC5410,author = {M. Gallet and C. Koutschan and Z. Li and G. Regensburger and J. Schicho and N. Villamizar},

title = {{Planar linkages following a prescribed motion}},

language = {english},

journal = {Math. Comp.},

volume = {87},

pages = {473--506},

isbn_issn = {ISSN: 1088-6842},

year = {2017},

refereed = {yes},

length = {34},

url = {http://www.ams.org/journals/mcom/2017-86-303/S0025-5718-2016-03120-8/}

}

[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]@

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/}

}

**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/}

}