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

    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
      to appear
      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
    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