Computational Mathematics

📝 Publications and preprints

1. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2024). New Ramsey Multiplicity Bounds and Search Heuristics. Foundations of Computational Mathematics. DOI: 10.1007/s10208-024-09675-6 [arXiv] [code]
   [BibTeX]

   @article{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics,
     year = {2024},
     journal = {Foundations of Computational Mathematics},
     doi = {10.1007/s10208-024-09675-6},
     archiveprefix = {arXiv},
     eprint = {2206.04036},
     primaryclass = {math.CO},
     author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
     title = {New Ramsey Multiplicity Bounds and Search Heuristics},
     code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
   }

2. Kiem, A., Pokutta, S., and Spiegel, C. (2024). The 4-color Ramsey Multiplicity of Triangles. Proceedings of Discrete Mathematics Days. [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2023_KiemPokuttaSpiegel_4colorramsey,
     year = {2024},
     booktitle = {Proceedings of Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_3.pdf},
     archiveprefix = {arXiv},
     eprint = {2312.08049},
     primaryclass = {math.CO},
     author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
     title = {The 4-color Ramsey Multiplicity of Triangles},
     code = {https://github.com/FordUniver/kps_trianglemult}
   }

3. Kiem, A., Pokutta, S., and Spiegel, C. (2024). Categorification of Flag Algebras. Proceedings of Discrete Mathematics Days. [URL]
   [BibTeX]

   @inproceedings{2024_KiemPokuttaSpiegel_Categorificationflagalgebras,
     year = {2024},
     booktitle = {Proceedings of Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_47.pdf},
     author = {Kiem, Aldo and Pokutta, Sebastian and Spiegel, Christoph},
     title = {Categorification of Flag Algebras}
   }

4. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings. Geombinatorics Quarterly, XXXIV. [URL] [arXiv]
   [BibTeX]

   @article{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion,
     year = {2024},
     journal = {Geombinatorics Quarterly},
     volume = {XXXIV},
     url = {https://geombina.uccs.edu/past-issues/volume-xxxiv},
     archiveprefix = {arXiv},
     eprint = {2404.05509},
     author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
     title = {Extending the Continuum of Six-Colorings}
   }

5. Mundinger, K., Pokutta, S., Spiegel, C., and Zimmer, M. (2024). Extending the Continuum of Six-Colorings. Proceedings of Discrete Mathematics Days. [URL] [arXiv]
   [BibTeX]

   @inproceedings{2024_MundingerPokuttaSpiegelZimmer_SixcoloringsExpansion:1,
     year = {2024},
     booktitle = {Proceedings of Discrete Mathematics Days},
     url = {https://dmd2024.web.uah.es/files/abstracts/paper_27.pdf},
     archiveprefix = {arXiv},
     eprint = {2404.05509},
     author = {Mundinger, Konrad and Pokutta, Sebastian and Spiegel, Christoph and Zimmer, Max},
     title = {Extending the Continuum of Six-Colorings}
   }

6. Parczyk, O., and Spiegel, C. (2024). An Unsure Note on an Un-Schur Problem. [arXiv]
   [BibTeX]

   @misc{2024_ParczykSpiegel_UnSchur,
     archiveprefix = {arXiv},
     eprint = {2410.22024},
     primaryclass = {math.CO},
     year = {2024},
     author = {Parczyk, Olaf and Spiegel, Christoph},
     title = {An Unsure Note on an Un-Schur Problem}
   }

7. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2023). Fully Computer-assisted Proofs in Extremal Combinatorics. Proceedings of AAAI Conference on Artificial Intelligence. DOI: 10.1609/aaai.v37i10.26470 [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:1,
     year = {2023},
     booktitle = {Proceedings of AAAI Conference on Artificial Intelligence},
     doi = {10.1609/aaai.v37i10.26470},
     url = {https://ojs.aaai.org/index.php/AAAI/article/view/26470},
     archiveprefix = {arXiv},
     eprint = {2206.04036},
     primaryclass = {math.CO},
     author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
     title = {Fully Computer-assisted Proofs in Extremal Combinatorics},
     code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
   }

8. Rué, J. J., and Spiegel, C. (2023). The Rado Multiplicity Problem in Vector Spaces Over Finite Fields. Proceedings of European Conference on Combinatorics. DOI: 10.5817/CZ.MUNI.EUROCOMB23-108 [URL] [arXiv] [code]
   [BibTeX]

   @inproceedings{2023_RueSpiegel_Radomultiplicity,
     year = {2023},
     booktitle = {Proceedings of European Conference on Combinatorics},
     doi = {10.5817/CZ.MUNI.EUROCOMB23-108},
     url = {https://journals.muni.cz/eurocomb/article/view/35642},
     archiveprefix = {arXiv},
     eprint = {2304.00400},
     primaryclass = {math.CO},
     author = {Rué, Juan José and Spiegel, Christoph},
     title = {The Rado Multiplicity Problem in Vector Spaces Over Finite Fields},
     code = {https://github.com/FordUniver/rs_radomult_23}
   }

9. Kamčev, N., and Spiegel, C. (2022). Another Note on Intervals in the Hales-Jewett Theorem. Electronic Journal of Combinatorics, 29(1). DOI: 10.37236/9400 [URL] [arXiv]
   [BibTeX]

   @article{2018_KamcevSpiegel_Halesjewettintervals,
     year = {2022},
     journal = {Electronic Journal of Combinatorics},
     volume = {29},
     number = {1},
     doi = {10.37236/9400},
     url = {https://combinatorics.org/ojs/index.php/eljc/article/view/v29i1p62},
     archiveprefix = {arXiv},
     eprint = {1811.04628},
     primaryclass = {math.CO},
     author = {Kamčev, Nina and Spiegel, Christoph},
     title = {Another Note on Intervals in the Hales-Jewett Theorem}
   }

10. Braun, G., Pokutta, S., and Weismantel, R. (2022). Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections. [arXiv] [slides] [video]
    [BibTeX]

    @misc{2022_BraunPokuttaWeismantel_Alternatingminimization,
      archiveprefix = {arXiv},
      eprint = {2212.02933},
      primaryclass = {math.OC},
      year = {2022},
      author = {Braun, Gábor and Pokutta, Sebastian and Weismantel, Robert},
      title = {Alternating Linear Minimization: Revisiting von Neumann’s Alternating Projections},
      slides = {https://pokutta.com/slides/20230327-icerm.pdf},
      video = {https://icerm.brown.edu/programs/sp-s23/w2/#schedule-item-4945}
    }

11. Parczyk, O., Pokutta, S., Spiegel, C., and Szabó, T. (2022). New Ramsey Multiplicity Bounds and Search Heuristics. Proceedings of Discrete Mathematics Days. [arXiv] [code]
    [BibTeX]

    @inproceedings{2022_ParczykPokuttaSpiegelSzabo_Ramseymultiplicityheuristics:2,
      year = {2022},
      booktitle = {Proceedings of Discrete Mathematics Days},
      archiveprefix = {arXiv},
      eprint = {2206.04036},
      primaryclass = {math.CO},
      author = {Parczyk, Olaf and Pokutta, Sebastian and Spiegel, Christoph and Szabó, Tibor},
      title = {New Ramsey Multiplicity Bounds and Search Heuristics},
      code = {https://zenodo.org/record/6602512#.YyvFhi8Rr5g}
    }

12. Cao-Labora, G., Rué, J. J., and Spiegel, C. (2021-10). An Erdős-Fuchs Theorem for Ordered Representation Functions. Ramanujan Journal, 56, 183–2091. DOI: 10.1007/s11139-020-00326-2 [URL] [arXiv]
    [BibTeX]

    @article{2019_CaolaboraRueSpiegel_Erdosfuchs,
      year = {2021-10},
      journal = {Ramanujan Journal},
      volume = {56},
      pages = {183-2091},
      doi = {10.1007/s11139-020-00326-2},
      url = {https://link.springer.com/article/10.1007/s11139-020-00326-2},
      archiveprefix = {arXiv},
      eprint = {1911.12313},
      primaryclass = {math.NT},
      author = {Cao-Labora, Gonzalo and Rué, Juan José and Spiegel, Christoph},
      title = {An Erdős-Fuchs Theorem for Ordered Representation Functions}
    }

13. Fabian, D., Rué, J. J., and Spiegel, C. (2021-08). On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers. Journal of Combinatorial Theory, Series A, 182. DOI: 10.1016/j.jcta.2021.105460 [URL] [arXiv]
    [BibTeX]

    @article{2019_FabianRueSpiegel_Strongsidonsets,
      year = {2021-08},
      journal = {Journal of Combinatorial Theory, Series A},
      volume = {182},
      doi = {10.1016/j.jcta.2021.105460},
      url = {https://sciencedirect.com/science/article/abs/pii/S0097316521000595},
      archiveprefix = {arXiv},
      eprint = {1911.13275},
      primaryclass = {math.CO},
      author = {Fabian, David and Rué, Juan José and Spiegel, Christoph},
      title = {On Strong Infinite Sidon and Bₕ Sets and Random Sets of Integers}
    }

14. Corsten, J., Mond, A., Pokrovskiy, A., Spiegel, C., and Szabó, T. (2020-10). On the Odd Cycle Game and Connected Rules. European Journal of Combinatorics, 89. DOI: 10.1016/j.ejc.2020.103140 [URL] [arXiv]
    [BibTeX]

    @article{2019_CorstenEtAl_Oddcyclegame,
      year = {2020-10},
      journal = {European Journal of Combinatorics},
      volume = {89},
      doi = {10.1016/j.ejc.2020.103140},
      url = {https://sciencedirect.com/science/article/abs/pii/S0195669820300615},
      archiveprefix = {arXiv},
      eprint = {1906.04024},
      primaryclass = {math.CO},
      author = {Corsten, Jan and Mond, Adva and Pokrovskiy, Alexey and Spiegel, Christoph and Szabó, Tibor},
      title = {On the Odd Cycle Game and Connected Rules}
    }

15. Rué, J. J., and Spiegel, C. (2020). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Revista Matemática Iberoamericana, 36(7), 2107–2119. DOI: 10.4171/RMI/1193 [URL] [arXiv]
    [BibTeX]

    @article{2018_RueSpiegel_Srkzyss,
      year = {2020},
      journal = {Revista Matemática Iberoamericana},
      volume = {36},
      number = {7},
      pages = {2107-2119},
      doi = {10.4171/RMI/1193},
      url = {https://ems.press/journals/rmi/articles/16818},
      archiveprefix = {arXiv},
      eprint = {1802.07597},
      primaryclass = {math.CO},
      author = {Rué, Juan José and Spiegel, Christoph},
      title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms}
    }

16. Candela, P., Serra, O., and Spiegel, C. (2020). A Step Beyond Freĭman’s Theorem for Set Addition Modulo a Prime. Journal De Théorie Des Nombres De Bordeaux, 32(1), 275–289. DOI: 10.5802/jtnb.1122 [URL] [arXiv]
    [BibTeX]

    @article{2019_CandelaSerraSpiegel_Fremantheorem,
      year = {2020},
      journal = {Journal de Théorie des Nombres de Bordeaux},
      volume = {32},
      number = {1},
      pages = {275-289},
      doi = {10.5802/jtnb.1122},
      url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_1_275_0/},
      archiveprefix = {arXiv},
      eprint = {1805.12374},
      primaryclass = {math.CO},
      author = {Candela, Pablo and Serra, Oriol and Spiegel, Christoph},
      title = {A Step Beyond Freĭman's Theorem for Set Addition Modulo a Prime}
    }

17. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2019-09). On the Optimality of the Uniform Random Strategy. Random Structures & Algorithms, 55(2), 371–401. DOI: 10.1002/rsa.20829 [URL] [arXiv]
    [BibTeX]

    @article{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy,
      year = {2019-09},
      journal = {Random Structures & Algorithms},
      volume = {55},
      number = {2},
      pages = {371-401},
      doi = {10.1002/rsa.20829},
      url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/rsa.20829},
      archiveprefix = {arXiv},
      eprint = {1711.07251},
      primaryclass = {math.CO},
      author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
      title = {On the Optimality of the Uniform Random Strategy}
    }

18. Freĭman, G. A., Serra, O., and Spiegel, C. (2019). Additive Volume of Sets Contained in Few Arithmetic Progressions. INTEGERS, 19. [URL] [arXiv]
    [BibTeX]

    @article{2018_FreimanSerraSpiegel_Additivevolumearithmeticprogressions,
      year = {2019},
      journal = {INTEGERS},
      volume = {19},
      url = {https://math.colgate.edu/~integers/t34/t34.mail.html},
      archiveprefix = {arXiv},
      eprint = {1808.08455},
      primaryclass = {math.NT},
      author = {Freĭman, Gregory A. and Serra, Oriol and Spiegel, Christoph},
      title = {Additive Volume of Sets Contained in Few Arithmetic Progressions}
    }

19. Salia, N., Spiegel, C., Tompkins, C., and Zamora, O. (2019). Independent Chains in Acyclic Posets. [arXiv]
    [BibTeX]

    @misc{2019_SaliaSpiegelTompkinsZamora_Independentchainsacyclicposets,
      archiveprefix = {arXiv},
      eprint = {1912.03288},
      primaryclass = {math.CO},
      year = {2019},
      author = {Salia, Nika and Spiegel, Christoph and Tompkins, Casey and Zamora, Oscar},
      title = {Independent Chains in Acyclic Posets}
    }

20. Rué, J. J., Spiegel, C., and Zumalacárregui, A. (2018). Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets. Mathematische Zeitschrift, 288, 333–360. DOI: 10.1007/s00209-017-1891-2 [URL] [arXiv]
    [BibTeX]

    @article{2012_RueSpiegelZumalacarregui_ThresholdfunctionsPoissonconvergence,
      year = {2018},
      journal = {Mathematische Zeitschrift},
      month = feb,
      volume = {288},
      pages = {333-360},
      doi = {10.1007/s00209-017-1891-2},
      url = {https://link.springer.com/article/10.1007/s00209-017-1891-2},
      archiveprefix = {arXiv},
      eprint = {1212.5496},
      primaryclass = {math.CO},
      author = {Rué, Juan José and Spiegel, Christoph and Zumalacárregui, Ana},
      title = {Threshold Functions and Poisson Convergence for Systems of Equations in Random Sets}
    }

21. Rué, J. J., and Spiegel, C. (2018). On a Problem of Sárközy and Sós for Multivariate Linear Forms. Proceedings of Discrete Mathematics Days. [URL] [arXiv]
    [BibTeX]

    @inproceedings{2018_RueSpiegel_Srkzyss:1,
      year = {2018},
      booktitle = {Proceedings of Discrete Mathematics Days},
      url = {https://congreso.us.es/dmd2018/wp-content/uploads/2018/05/DMD2018_paper_21.pdf},
      archiveprefix = {arXiv},
      eprint = {1802.07597},
      primaryclass = {math.CO},
      author = {Rué, Juan José and Spiegel, Christoph},
      title = {On a Problem of Sárközy and Sós for Multivariate Linear Forms}
    }

22. Kusch, C., Rué, J. J., Spiegel, C., and Szabó, T. (2017). Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games. Proceedings of European Conference on Combinatorics. [URL] [arXiv]
    [BibTeX]

    @inproceedings{2017_KuschRueSpiegelSzabo_Uniformrandomstrategy:1,
      year = {2017},
      booktitle = {Proceedings of European Conference on Combinatorics},
      url = {https://dmg.tuwien.ac.at/eurocomb2017/index.php/accepted-papers/},
      archiveprefix = {arXiv},
      eprint = {1711.07251},
      primaryclass = {math.CO},
      author = {Kusch, Christopher and Rué, Juan José and Spiegel, Christoph and Szabó, Tibor},
      title = {Random Strategies Are Nearly Optimal for Generalized Van Der Waerden Games}
    }

23. Spiegel, C. (2017). A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems. Electronic Journal of Combinatorics, 24(3). DOI: 10.37236/6730 [URL] [arXiv]
    [BibTeX]

    @article{2017_Spiegel_Sparsesupersaturation,
      year = {2017},
      journal = {Electronic Journal of Combinatorics},
      volume = {24},
      number = {3},
      doi = {10.37236/6730},
      url = {https://combinatorics.org/ojs/index.php/eljc/article/view/v24i3p38},
      archiveprefix = {arXiv},
      eprint = {1701.01631},
      primaryclass = {math.CO},
      author = {Spiegel, Christoph},
      title = {A Note on Sparse Supersaturation and Extremal Results for Linear Homogeneous Systems}
    }

24. Böttcher, J., Frankl, N., Cecchelli, D. M., Skokan, J., and Parczyk, O. Graphs with Large Minimum Degree and No Small Odd Cycles Are 3-colourable. [arXiv]
    [BibTeX]

    @misc{2023_BoettcherEtAl_Graphs3colourable,
      archiveprefix = {arXiv},
      eprint = {2302.01875},
      author = {Böttcher, Julia and Frankl, Nóra and Cecchelli, Domenico Mergoni and Skokan, Jozef and Parczyk, Olaf},
      title = {Graphs with Large Minimum Degree and No Small Odd Cycles Are 3-colourable}
    }

25. Mattos, L., Cecchelli, D. M., and Parczyk, O. On Product Schur Triples in the Integers. [arXiv]
    [BibTeX]

    @misc{2023_MattosDomenicoParczyk_Productschurtriples,
      archiveprefix = {arXiv},
      eprint = {2311.18796},
      author = {Mattos, Letícia and Cecchelli, Domenico Mergoni and Parczyk, Olaf},
      title = {On Product Schur Triples in the Integers}
    }

26. Díaz, A. E., Gupta, P., Cecchelli, D. M., Parczyk, O., and Sgueglia, A. Dirac’s Theorem for Graphs of Bounded Bandwidth. [arXiv]
    [BibTeX]

    @misc{2024_AlbertoEtAl_Diractheorembandwidth,
      archiveprefix = {arXiv},
      eprint = {2407.05889},
      author = {Díaz, Alberto Espuny and Gupta, Pranshu and Cecchelli, Domenico Mergoni and Parczyk, Olaf and Sgueglia, Amedeo},
      title = {Dirac's Theorem for Graphs of Bounded Bandwidth}
    }

27. Illingworth, F., Lang, R., Müyesser, A., Parczyk, O., and Sgueglia, A. Spanning Spheres in Dirac Hypergraphs. [arXiv]
    [BibTeX]

    @misc{2024_FreddieEtAl_Spanningspheresdirac,
      archiveprefix = {arXiv},
      eprint = {2407.06275},
      author = {Illingworth, Freddie and Lang, Richard and Müyesser, Alp and Parczyk, Olaf and Sgueglia, Amedeo},
      title = {Spanning Spheres in Dirac Hypergraphs}
    }