Publications

Open Science is crucial. Therefore the results of my research are freely available to the public. The arXiv versions are updated to the same text as the commercially published version and have much better typesetting. You should generally prefer arXiv versions. Please e-mail me if you really need the commercially published versions and can’t access it.

My author profiles on ZBMath, MathSciNet, and Google Scholar.

Preprints

  1. Trinomial containment in polynomial ideals is undecidable,
    Tobias Boege, Anna Hofer, and Thomas Kahle
    2026
    arXiv Lean

Peer-reviewed articles

  1. Arrangements and Likelihood,
    Thomas Kahle, Lukas Kühne, Leonie Mühlherr, Bernd Sturmfels, and Maximilian Wiesmann
    Vietnam Journal of Mathematics, 2026
    DOI arXiv
  2. The Likelihood Correspondence,
    Thomas Kahle, Hal Schenck, Bernd Sturmfels, and Maximilian Wiesmann
    Foundations of Computational Mathematics, 2026
    DOI arXiv
  3. Lattice supported distributions and graphical models,
    Thomas Kahle and Seth Sullivant
    to appear in Proc. AMS, 2025
    arXiv
  4. Efficiently deciding if an ideal is toric after a linear coordinate change,
    Thomas Kahle and Julian Vill
    SIAM Journal on Applied Algebra and Geometry, 2025
    DOI arXiv
  5. Optimal designs for discrete choice models via graph Laplacians,
    Frank Röttger, Thomas Kahle, and Rainer Schwabe
    Journal of Statistical Theory and Practice, 2025
    DOI arXiv
  6. Liftings of polynomial systems decreasing the mixed volume,
    Christopher Borger, Thomas Kahle, Andreas Kretschmer, Sebastian Sager, and Jonas Schulze
    Proceedings of the Einstein Semester Varieties, Polyhedra, Computation, 2025
    DOI arXiv
  7. Extreme Values of Permutation Statistics,
    Philip Dörr and Thomas Kahle
    Electronic Journal of Combinatorics, 2024
    DOI arXiv
  8. No short polynomials vanish on bounded rank matrices,
    Jan Draisma, Thomas Kahle, and Finn Wiersig
    Bulletin London Math. Soc., 2023
    DOI arXiv
  9. Binomial edge ideals of cographs,
    Thomas Kahle and Jonas Krüsemann
    Rev. Un. Mat. Argentina, 2022
    DOI arXiv
  10. Invariant chains in algebra and discrete geometry,
    Thomas Kahle, Dinh Van Le, and Tim Römer
    SIAM Discrete Math., 2022
    DOI arXiv
  11. The geometry of Gaussian double Markovian distributions,
    Tobias Boege, Thomas Kahle, Andreas Kretschmer, and Frank Röttger
    Scandinavian Journal of Statistics, 2022
    DOI arXiv
  12. Hilbert–Poincaré series of parity binomial edge ideals and permanental ideals of complete graph,
    Do Trong Hoang and Thomas Kahle
    Collecteana Mathematica, 2021
    DOI arXiv
  13. The semi-algebraic geometry of optimal designs for the Bradley–Terry model,
    Thomas Kahle, Frank Röttger, and Rainer Schwabe
    Algebraic Statistics, 2021
    DOI arXiv
  14. Construction Methods for Gaussoids,
    Tobias Boege and Thomas Kahle
    Kybernetika, 2020
    DOI arXiv
  15. Counting inversions and descents of random elements in finite Coxeter groups,
    Thomas Kahle and Christian Stump
    Math. of Computation, 2020
    DOI arXiv
  16. Sums of squares in Macaulay2,
    Diego Cifuentes, Thomas Kahle, and Pablo A Parrilo
    Journal of Software for Algebra and Geometry, 2020
    DOI arXiv
  17. Linear syzygies, hyperbolic Coxeter groups and regularity,
    Alexandru Constantinescu, Thomas Kahle, and Matteo Varbaro
    Compositio Mathematica, 2019
    DOI arXiv
  18. Multistationarity in the space of total concentrations for systems that admit a monomial parametrization,
    Carsten Conradi, Alexandru Iosif, and Thomas Kahle
    Bulletin Math. Biology, 2019
    DOI arXiv
  19. The Geometry of Gaussoids,
    Tobias Boege, Alessio D’Alì, Thomas Kahle, and Bernd Sturmfels
    Foundations of Computational Mathematics, 2019
    DOI arXiv
  20. Obstructions to combinatorial formulas for plethysm,
    Thomas Kahle and Mateusz Michałek
    Electronic Journal of Combinatorics, 2018
    DOI arXiv
  21. Veronesean almost binomial almost complete intersections,
    Thomas Kahle and André Wagner
    Rendiconti dell’Istituto di Matematica dell’Università di Trieste, 2018
    DOI arXiv
  22. Finding binomials in polynomial ideals,
    Anders Jensen, Thomas Kahle, and Lukas Katthän
    Research in the Mathematical Sciences, 2017
    DOI arXiv
  23. The geometry of rank-one tensor completion,
    Thomas Kahle, Kaie Kubjas, Mario Kummer, and Zvi Rosen
    SIAM Journal on Applied Algebra and Geometry, 2017
    DOI arXiv
  24. Algebraic geometry of Poisson regression,
    Thomas Kahle, Kai-Friederike Oelbermann, and Rainer Schwabe
    Journal of Algebraic Statistics, 2016
    DOI arXiv
  25. Eigenschemes and the Jordan canonical form,
    Hirotachi Abo, David Eklund, Thomas Kahle, and Chris Peterson
    Linear Algebra and its Applications, 2016
    DOI arXiv
  26. Irreducible decomposition of binomial ideals,
    Thomas Kahle, Ezra Miller, and Christopher O’Neill
    Compositio Mathematica, 2016
    DOI arXiv
  27. Linear syzygies, flag complexes, and regularity,
    Alexandru Constantinescu, Thomas Kahle, and Matteo Varbaro
    Collectanea Mathematica, 2016
    DOI arXiv
  28. Parity binomial edge ideals,
    Thomas Kahle, Camilo Sarmiento, and Tobias Windisch
    Journal of Algebraic Combinatorics, 2016
    DOI arXiv
  29. Detecting binomiality,
    Carsten Conradi and Thomas Kahle
    Advances in Applied Mathematics, 2015
    DOI arXiv
  30. Plethysm and lattice point counting,
    Thomas Kahle and Mateusz Michałek
    Foundations of Computational Mathematics, 2015
    DOI arXiv
  31. Decompositions of Commutative Monoid Congruences and Binomial Ideals,
    Thomas Kahle and Ezra Miller
    Algebra & Number Theory, 2014
    DOI arXiv
  32. Equivariant lattice generators and Markov bases,
    Thomas Kahle, Robert Krone, and Anton Leykin
    Proceedings of ISSAC 2014, 2014
    DOI arXiv
  33. Generic and special constructions of pure O-sequences,
    Alexandru Constantinescu, Thomas Kahle, and Matteo Varbaro
    Bulletin of the London Mathematical Society, 2014
    DOI arXiv
  34. Multigraded commutative algebra of graph decompositions,
    Alexander Engström, Thomas Kahle, and Seth Sullivant
    Journal of Algebraic Combinatorics, 2014
    DOI arXiv
  35. Positive margins and primary decomposition,
    Thomas Kahle, Johannes Rauh, and Seth Sullivant
    Journal of Commutative Algebra, 2014
    DOI arXiv
  36. Toric fiber products versus Segre products,
    Thomas Kahle and Johannes Rauh
    Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2014
    DOI arXiv
  37. Decompositions of Binomial Ideals,
    Thomas Kahle
    Journal of Software for Algebra and Geometry, 2012
    DOI arXiv
  38. Support Sets in Exponential Families and Oriented Matroid Theory,
    Johannes Rauh, Thomas Kahle, and Nihat Ay
    International Journal of Approximate Reasoning, 2011
    DOI arXiv
  39. Binomial Edge Ideals and Conditional Independence Statements,
    Jürgen Herzog, Takayuki Hibi, Freyja Hreinsdóttir, Thomas Kahle, and Johannes Rauh
    Advances in Applied Mathematics, 2010
    DOI arXiv Lean
  40. Decompositions of Binomial Ideals,
    Thomas Kahle
    Annals of the Institute of Statistical Mathematics, 2010
    DOI arXiv
  41. Neighborliness of Marginal Polytopes,
    Thomas Kahle
    Contributions to Algebra and Geometry, 2010
    arXiv
  42. Quantifying structure in networks,
    Eckehard Olbrich, Thomas Kahle, Nils Bertschinger, Nihat Ay, and Jürgen Jost
    European Physical Journal B, 2010
    DOI arXiv
  43. Complexity Measures from Interaction Structures,
    Thomas Kahle, Eckehard Olbrich, Jürgen Jost, and Nihat Ay
    Physical Review E, 2009
    DOI arXiv
  44. Hierarchical Models, Marginal Polytopes, and Linear Codes,
    Thomas Kahle, Walter Wenzel, and Nihat Ay
    Kybernetika, 2009
    DOI arXiv

Software and Data

  1. The Markov Bases Database,
    Thomas Kahle and Johannes Rauh
    2010
  2. cipi—Computing Information Projections Iterativly,
    Lydia Steiner and Thomas Kahle
    2008

Conference and Book contributions

  1. Algebraic Aspects of Conditional Independence and Graphical Models,
    Thomas Kahle, Johannes Rauh, and Seth Sullivant
    In Handbook of Graphical Models, 2017
    arXiv
  2. On the Feasibility of Semi-algebraic Sets in Poisson Regression,
    Thomas Kahle
    In Mathematical Software – ICMS 2016: 5th International Conference, Berlin, Germany, July 11-14, 2016, Proceedings, 2016
    DOI arXiv
  3. Support sets of distributions with given interaction Structure,
    Thomas Kahle and Nihat Ay
    In Proceedings of the WUPES 2006, 2006

Other

  1. Wissenschaftskommunikation im Fediverse,
    Thomas Kahle
    Mitteilungen der Deutschen Mathematiker-Vereinigung, 2026
    DOI
  2. The 4-Sample Theorem on planar graphs,
    Carlos Améndola and Thomas Kahle
    2026
    DOI HTML
  3. Pi ist genau 3,
    Thomas Kahle and Petra Schwer
    Mitteilungen der Deutschen Mathematiker-Vereinigung, 2021
    DOI
  4. Review of “Algebraic Statistics” by Seth Sullivant,
    Thomas Kahle
    Bull. AMS, 2021
  5. Short polynomials in determinantal ideals,
    Thomas Kahle and Finn Wiersig
    arXiv only, 2021
    This paper was superseded by https://arxiv.org/abs/2112.11764
    arXiv
  6. Review of “Algebraic Statistics” by Seth Sullivant,
    Thomas Kahle
    DMV Jahresbericht, 2019
  7. Abschlussarbeiten mit Publikum,
    Thomas Kahle and Kai-Friederike Oelbermann
    In Science who cares - Sammelband zum Universitätsjubiläum, 2010
    in German