• T. Kahle, L. Kühne, L. Mühlherr, B. Sturmfels, M. Wiesmann Arrangements and Likelihood, arXiv:2411.09508.
• T. Kahle, S. Sullivant Lattice supported distributions and graphical models, arXiv:2411.03139.
• T. Kahle, J. Vill Efficiently deciding if an ideal is toric after a linear coordinate change, arXiv:2408.14323.
• F. Röttger, T. Kahle, R. Schwabe Optimal designs for discrete choice models via graph Laplacians, arXiv:2208.08926.

The results of my research are freely available to the public. Please e-mail me if you have trouble accessing one of my papers. I try to keep the arXiv versions up to date and often they also have better typesetting than the published versions.

• C. Borger, T. Kahle, A. Kretschmer, S. Sager, J. Schulze Liftings of polynomial systems decreasing the mixed volume, arXiv:2105:10714, to appear in Proceedings of the Einstein Semester Varieties, Polyhedra, Computation.
• P. Dörr, T. Extreme Values of Permutation Statistics, Electronic Journal of Combinatorics 31 (3) #P3.10 (2024) (Diamond OA-Link to journal page), arXiv:2205.01426.
• J. Draisma, T. Kahle, F. Wiersig No short polynomials vanish on bounded rank matrices, Bulletin LMS 55 (4) (2023), pp. 1791-1807 (DEAL OpenAccess Link), arXiv:2112.11764.
• T. Boege, T. Kahle, A. Kretschmer, F. Röttger The geometry of Gaussian double Markovian distributions, appered online in Scandinavian Journal of Statistics. arXiv:2107:00134. (The arXiv version is better. Wiley's copyediting process introduced new typos and oddities).
• T. Kahle, D. Van Le, T. Römer Invariant chains in algebra and discrete geometry, SIAM J Discrete Math 36 (2) (2022), pp. 975-999. arxiv:2010.15163, Journal Link.
• T. Kahle, J. Krüsemann Binomial edge ideals of cographs, Revista de la Unión Matemática Argentina. 63 (2) (2022) pp. 305–316. Diamond OA Link.
• T. Kahle, F. Röttger, R. Schwabe The semi-algebraic geometry of optimal designs for the Bradley-Terry model, Algebraic Statistics 12 (1) (2021) pp. 97-114. Journal link (OpenAccess), arXiv:1901.02375.
• D.T. Hoang, T. Kahle Hilbert-Poincaré series of parity binomial edge ideals and permanental ideals of complete graphs, Collectanea Mathematica 72 (3) (2021) pp. 471-459. DEAL OpenAccess Link. arXiv:2003.00977.
• D. Cifuentes, T. Kahle, P. A. Parrilo Sums of squares in Macaulay2, Journal of Software for Algebra and Geometry 10 (1) (2020) pp. 17-24. Open Access Link.
• T. Boege, T.Kahle Construction methods for gaussoids, Kybernatika 56 (6), special issue dedicated to the memory of Fero Matus (2020) pp 1045-1062. OpenAccess Journal Link. arXiv:1902.11260.
• C. Conradi, A. Iosif, T. Kahle Multistationarity in the space of total concentrations for systems that admit a monomial parametrization, appeared online in Bulletin of Mathematical Biology. arXiv:1810.08152, Journal link.
• T. Kahle, C. Stump Counting inversions and descents of random elements in finite Coxeter groups, to appear in Mathematics of Computation. arXiv:1802.01389. Journal Link.
• A. Constantinescu, T. Kahle, M. Varbaro Linear syzygies, hyperbolic Coxeter groups and regularity, Compositio Mathematica 166 (5) (2019) pp. 1076-1097. Journal link. arXiv:1705.01802.
• T. Boege, A. D'Alì, T. Kahle, B. Sturmfels The geometry of gaussoids, J. Found. Comp. Math 19 (4) (2019) pp. 775-812 Journal Link. YouTube Version. arXiv:1710.07175.
• T. Kahle, A. Wagner Veronesean almost binomial almost complete intersections, Rendiconti dell'Istituto di Matematica dell'Università di Trieste 50 (2018) pp. 75-79, Open Access Journal Link. arXiv:1608.03499.
• T. Kahle, M. Michałek, Obstructions to combinatorial formulas for plethysm Electronic Journal of Combinatorics 25 (1) #P.41 (2018). arXiv:1507.07131.
• A. Jensen, T. Kahle, L. Katthän Finding binomials in polynomial ideals, Research in the Mathematical Sciences 4 (16) (2017) 12p. open access journal link, arXiv:1607:02135, slides from Magdeburg.
• T. Kahle, K. Kubjas, M. Kummer, Z. Rosen The geometry of rank-one tensor completion, SIAM Journal on Applied Algebra and Geometry 1 (1) (2017), pp 200-221. DOI Link, download author copy, arXiv:1605.01678, slides from Berlin.
• T. Kahle, K.-F. Oelbermann, R. Schwabe, Algebraic geometry of Poisson regression Journal of Algebraic Statistics 7 (2016) pp. 29–44. open access link. arXiv:1510.05261.
• H. Abo, D. Eklund, T. Kahle, C. Peterson, Eigenschemes and the Jordan canonical form. Linear Algebra and its Applications 496 (2016), pp. 121-151 Elsevier link, arXiv:1506.08257.
• T. Kahle, C. Sarmiento, T. Windisch Parity binomial edge ideals. Journal of Algebraic Combinatorics 44 (2016), pp. 99-117 Springer Link. arXiv:1503.00584.
• T. Kahle, E. Miller, C. O'Neill Irreducible decomposition of binomial ideals. Compositio Mathematica 152 (6), (2016), pp. 1319-1332. Cambridge Univ. Press Link. arXiv:1503.02607.
• C. Conradi, T. Kahle Detecting binomiality. Adv. Appl. Math. 71 (2015), pp. 52-67. Elsevier link, arXiv:1502.04893.
• T. Kahle, M. Michałek, Plethysm and lattice point counting. Found. Comp. Math 13 (5)(2016). arXiv:1408.5708.
• A. Constantinescu, T. Kahle, M. Varbaro Linear syzygies, flag complexes, and regularity. Collectanea Mathematica 63 (3) (2016), pp. 357–362. arXiv:1410.4582.
• T. Kahle, R. Krone, A. Leykin Equivariant lattice generators and Markov bases Proc. ISSAC 2014, Kobe, Japan, arXiv:1401.0397, slides from Daejeon.
• T. Kahle, E. Miller Decompositions of commutative monoid congruences and binomial ideals. Algebra and Number Theory 8 (6)(2014), pp 1297–1364, arxiv:1107.4699. See me talk about this paper or look at the slides from Marburg.
• T. Kahle, J. Rauh Toric fiber products versus Segre products Abh. Math. Sem. Univ. Hamburg, 84 (2), (2014), pp. 187-201, Download from Springer, arXiv:1307.4029.
• A. Constantinescu, T. Kahle, M. Varbaro Generic and special constructions of pure O-sequences Bulletin of the London Math. Soc 46 (2014), pp 924-942, Journal Link at OUP. arXiv:1212.3426, Slides from Osnabrück.
• T. Kahle, J. Rauh, S. Sullivant Positive Margins and primary decomposition. Journal of Commutative Algebra 6 (2), (2014), pp 173-208, arxiv:1201.2591.
• A. Engström, T. Kahle, S. Sullivant Multigraded commutative algebra of graph decompositions, Journal of Algebraic Combinatorics , 39 (2) (2014), pp. 335-372, SpringerLink, arxiv:1102.2601
• T. Kahle, Decompositions of Binomial Ideals open-access pdf, JSAG 4 (2012), pp. 1-5.
• J. Herzog, T. Hibi, F. Hreinsdottir, T. Kahle, J. Rauh, Binomial Edge Ideals and Conditional Independence Statements, Advances in Applied Mathematics 45 (2010), pp. 317-333 arxiv:0909.4717
• T. Kahle Decompositions of Binomial Ideals AISM 62 (4), (2010), p. 727-745 Springer link, arxiv:0906.4873
• J. Rauh, T. Kahle, N. Ay Support Sets in Exponential Families and Oriented Matroid Theory, Proc. WUPES'09, and Int. J. Approximate Reasoning 52 (5), (2011), 613-626, arxiv:0906.5462
• E.Olbrich, T.Kahle, N.Bertschinger, N. Ay, J.Jost Quantifying structure in networks, Eur. Phys. J. B 77, p. 239-247 (2010) arxiv:0912.4450
• T. Kahle Neighborliness of Marginal Polytopes Contributions to Algebra and Geometry 51 (1) p 45-56 (2010), arxiv:0809.0786
• T. Kahle, E.Olbrich, J. Jost, N. Ay Complexity Measures from Interaction Structures Phys. Rev. E 79, 026201 (2009) arxiv:0806.2552
• T. Kahle, W. Wenzel, N. Ay, Hierarchical Models, Marginal Polytopes, and Linear Codes, Kybernetika 45 (2) 189-208 (2009), arxiv:0805.1301

• T. Kahle, J. Rauh, S. Sullivant Algebraic Aspects of Conditional Independence and Graphical Models, Chapter 3 of forthcoming Handbook of Graphical Models arXiv:1705.07411.
• T. Kahle On the feasibility of semi-algebraic sets in Poisson regression in Proceedings ICMS 2016, Berlin, pp 142-147. SpringerLink. arXiv:1605.00265.
• T. Kahle, N. Ay. Support Sets of Distributions with Given Interaction Structure Proceedings of WUPES'06 (2006). Santa Fe Institute Working Paper 06-08-027. pdf

• T. Kahle, F. Wiersig Short polynomials in determinantal ideals, arXiv:2109.00578. This paper was superseded by https://arxiv.org/abs/2112.11764.
• Review of the book "Algebraic Statistics" by Seth Sullivant, in DMV Jahresbericht 121, 307–311 (2019), Journal link.
• And another review of "Algebraic Statistics" by Seth Sullivant, this time for Bulletin AMS 58 (2) 305-309 (2021).
• See me give an introduction to toric ideals in algebraic statistics
• T. Kahle On Boundaries of Statistical Models, PhD thesis at Leipzig University.
• K.-F. Oelbermann, T. Kahle, Abschlussarbeiten mit Publikum (German), in Science who cares - Sammelband zum Universitätsjubiläum
• Unmöglich oder Unwahrscheinlich (German) - Entry to "Klaus Tschira Preis fuer verständliche Wissenschaft"