Publications and Preprints -- Seth Sullivant


  1. Algebraic Statistics (in preparation)
  2. Lectures on Algebraic Statistics (with Mathias Drton and Bernd Sturmfels), Oberwolfach Seminar Series 39, Birkhauser, 2009
  3. Emerging Applications of Algebraic Geometry (edited with Mihai Putinar), IMA Series 149, Springer, 2008

Submitted Papers and Preprints

  1. Identifiability of phylogenetic parameters from k-mer data under the coalescent (with Chris Durden) 1705.06993
  2. Strongly robust toric ideals in codimension 2. 1610.07476
  3. Sequential importance sampling for the Ising model (with Jing Xi) 1410.4217

Papers in Press

  1. Algebraic aspects of conditional independence and graphical models. (with Thomas Kahle and Johannes Rauh). To appear in Handbook of Graphical Models, CRC Press (Editors: Mathis Drton, Steffen Lauritzen, Marloes Matthuis, Martin Wainwright). 1705.07411
  2. Algebraic tools for the analysis of state space models (with Nicolette Meshkat and Zvi Rosen) To appear in Proceedings of Mathematical Society of Japan, 2015 Summer Institute on Grobner bases 1609.07985
  3. The maximum likelihood threshold of a graph (with Elizabeth Gross) To appear in Bernoulli, 1404.6989

Papers in Print

  1. Statistically consistent k-mer methods for phylogenetic tree reconstruction (with Elizabeth Allman and John Rhodes) Journal of Computational Biology February 2017, 24(2): 153-171. 1511.01956 Supplementary Materials
  2. Unimodular binary hierarchical models (with Daniel I. Bernstein) Journal of Combinatorial Theory: Series B 123 (2017), 97–125. 1502.06131 Supplementary Materials
  3. Normal binary hierarchical models (with Daniel I. Bernstein) Experimental Mathematics 26 (2017), no. 2, 153–164. 1508.05461
  4. Matrix Schubert varieties and Gaussian conditional independence models (with Alex Fink and Jenna Rajchgot) Journal of Algebraic Combinatorics, 44 (2016), no. 4, 1009-1046. 1510.04124
  5. Lifting Markov bases and higher codimension toric fiber products (with Johannes Rauh) J. Symbolic Comput. 74 (2016), 276–307. 1404.6392
  6. Identifiability results for several classes of linear compartment models (with Nicolette Meshkat and Marisa Eisenberg) Bull. Math. Biol. 77 (2015), no. 8, 1620–1651. 1410.8587
  7. Bounds on the expected size of the maximum agreement subtree (with Daniel I. Bernstein, Lam Ho, Colby Long, Mike Steel, and Katherine St. John) SIAM J. Discrete Math. 29 (2015), no. 4, 2065–2074.1411.7338
  8. Tying up loose strands: the defining equations of the strand symmetric model (with Colby Long) J. Algebr. Stat. 6 (2015), no. 1, 17–23.1410.3344   Supplementary Materials
  9. Identifiability of Jukes-Cantor 3-tree mixtures (with Colby Long) Adv. in Appl. Math. 64 (2015), 89–110. 1406.7256 Supplementary Materials
  10. Distance-based phylogenetic algorithms around a polytomy (with Ruth Davidson) IEEE/ACM Transactions in Computational Biology and Bioinformatics 11 (2014) 325-335 1307.5908   Supplementary Materials
  11. Positive margins and primary decomposition. (with Thomas Kahle and Johannes Rauh) Journal of Commutative Algebra 6 (2), (2014), pp 173-208.1201.2591
  12. Structural identifiability of viscoelastic mechanical systems (with Adam Mahdi and Nicolette Meshkat) PLOS One 9 (2014): e864111 1308.4950
  13. Identifiable reparametrizations of linear compartment models (with Nicolette Meshkat) Journal of Symbolic Computation 63 (2014), 46–67.1305.5768
  14. Multigraded commutative algebra of graph decompositions. (with Alexander Engström and Thomas Kahle) J. Algebraic Combinatorics 39 (2014) no. 2, 335-372 1102.2601
  15. Graphical models in Macaulay2 (with Luis Garcia-Puente and Sonja Petrovic) Journal of Software for Algebra and Geometry 5 (2013)1208.6550 Code
  16. Positivity for Gaussian graphical models (with Jan Draisma and Kelli Talaska) Adv. in Appl. Math. 50 (2013), no. 5, 661–674. 1210.0390
  17. Polyhedral combinatorics of UPGMA cones (with Ruth Davidson) Adv. in Appl. Math. 50 (2013), no. 2, 327–338.1206.1621   Supplementary Materials
  18. When do phylogenetic mixture models mimic other phylogenetic models? (with Elizabeth Allman and John Rhodes) Systematic Biology (2012) 61 (6): 1049-1059 1202.2396
  19. The disentangling number for phylogenetic mixtures. SIAM Journal on Discrete Mathematics 26-2 (2012), pp. 856-859 1107.2880
  20. Identifiability of large phylogenetic mixture models. (with John Rhodes). Bull. Math. Biol. 74 (2012), no. 1, 212–231. 1011.4134
  21. Finite Gröbner bases in infinite dimensional polynomial rings and applications. (with Christopher Hillar). Advances in Mathematics 221 (2012) 1-25 0908.1777
  22. Geodesics in CAT(0) cubical complexes. (with Federico Ardila and Megan Owen). Advances in Applied Mathematics 48 (2012) 142-163 1101.2428
  23. Eulerian-Catalan numbers. (with Hoda Bidkhori). Electronic Journal of Combinatorics 18 no.1 (2011) #P187 1101.1108
  24. Global identifiability of linear structural equation models (with Mathias Drton and Rina Foygel), Annals of Statistics 39 (2011):865-886. 1003.1146
  25. Identifiability of two-tree mixtures for group-based models. (with Elizabeth Allman, Sonja Petrovic, and John Rhodes), IEEE/ACM Transactions in Computational Biology and Bioinformatics, 8 no. 3 (2011) 710-722. 0909.1854   Supplementary Materials
  26. Normal binary graph models. Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics, 64 no.4 (2010) 717-726 0906.1784
  27. Trek separation for Gaussian graphical models. (with Kelli Talaska and Jan Draisma), Annals of Statistics 38 no.3 (2010) 1665-1685 0812.1938
  28. Markov models for accumulating mutations.  (with Niko Beerenwinkel), Biometrika 96 no. 3 (2009) 645-661 0709.2646
  29. Prolongations and computational algebra.  (with Jessica Sidman), Canadian Journal of Mathematics 61 no. 4 (2009) 930-949 math.AC/0611696
  30. A Gröbner basis for the secant ideal of the second hypersimplex.  Journal of Commutative Algebra 1 no.2 (2009) 0804.2897
  31. Gaussian conditional independence relations have no finite complete characterization.  Journal of Pure and Applied Algebra, 213 (2009) 1502-1506 (special issue on Theoretical and Practical Effectivity of Gröbner Bases)  0704.2847
  32. Toric geometry of cuts and splits. (with Bernd Sturmfels) Michigan Mathematical Journal 57 (2008) 689-709 (special issue in honor of Mel Hochster) math.AC/0606683
  33. Algebraic geometry of Gaussian Bayesian networks. Adv. in Appl. Math. 40 (2008), no. 4, 482--513. 0704.0918
  34. Combinatorial symbolic powers. J. Algebra 319 (2008), no. 1, 115--142. math.AC/0608542
  35. Algebraic statistical models. (with Mathias Drton) Statist. Sinica 17 (2007), no. 4, 1273--1297.  math.ST/0703609
  36. Toric fiber products. J. Algebra 316 (2007), no. 2, 560--577. math.AC/0602052
  37. Algebraic factor analysis:  tetrads, pentads, and beyond.  (with Mathias Drton and Bernd Sturmfels),  Probability Theory and Related Fields  138 (2007), no. 3-4, 463--493.  math.ST/0509390
  38. A finiteness theorem for Markov bases of hierarchical models.   (with Serkan Hosten)   J. Combin. Theory Ser. A  114  (2007),  no. 2, 311--321.  math.CO/0401379
  39. Combinatorial secant varieties.  (with Bernd Sturmfels) Quarterly Journal of Pure and Applied Mathematics 2 (2006) 285-309  (Special issue in honor of Robert Macpherson) math.AC/0506223
  40. Compressed polytopes and statistical disclosure limitation.  Tohoku Math. J. (2)  58  (2006),  no. 3, 433--445. math.CO/0412535
  41. Sequential importance sampling for multiway tables.  (with Yuguo Chen and Ian Dinwoodie), Annals of Statistics (2006) 34 No. 1, 523-545  math.ST/0605615
  42. Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models. (with Nicholas Eriksson, Stephen E. Fienberg, and Alessandro Rinaldo),  Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006)  222-233 math.CO/0405044
  43. The space of compatible full conditionals is a unimodular toric variety.   (with Aleksandra Slavkovic), Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006) 196-209  math.AG/0405046
  44. Small contingency tables with large gaps.  SIAM Journal of Discrete Mathematics  18 (2005) no.4, 787-793  math.OC/0405038
  45. Toric ideals of phylogenetic invariants.  (with Bernd Sturmfels), Journal of Computational Biology 12 (2005) 204-228.   q-bio.PE/0402015
  46. Ideals of adjacent minors.  (with Serkan Hosten),  Journal of Algebra  277 (2004), 615-642   math.AC/0306318
  47. A divide-and-conquer algorithm for generating Markov bases of multi-way tables.  (with A. Dobra),  Computational Statistics  19 (2004), 347-366
  48. Markov bases of binary graph models.  (with Mike Develin), Annals of Combinatorics  7 (2003), 441-466 math.CO/0308280
  49. Gröbner bases and polyhedral geometry of reducible and cyclic models.  (with Serkan Hosten)  Journal of Combinatorial Theory: Series A 100 (2002) no. 2, 277-301

Conference Proceedings and Book Chapters

  1. Identifying causal effects with computer algebra (with Luis Garcia-Puente and Sarah Spielvogel) Uncertainty in Artificial Intelligence, Proceedings of the 26th Conferences, AUAI Press, 2010. 1007.3784
  2. Algebraic complexity of maximum likelihood estimation for bivariate missing data.  (with Serkan Hosten), Book chapter in the book Algebraic and Geometric Methods in Statistics, Cambridge University Press, 2009. ISBN-13: 9780521896191 arXiv:0709.0935.
  3. Phylogenetic algebraic geometry.  (with Nicholas Eriksson, Kristian Ranestad, and Bernd Sturmfels), in Projective Varieties with Unexpected Properties, edited by C. Ciliberto, et al.,  Walter de Gruyter, Berlin, 2005  math.AG/0407033
  4. Catalog of small trees.  (with Marta Casanellas and Luis Garcia-Puente), in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.
  5. The strand symmetric model.  (with Marta Casanellas), in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.


  1. Toric ideals in algebraic statistics, 2005 pdf. (Ph. D. Thesis, UC Berkeley)
  2. Algebraic geometry and combinatorics of hierarchical models, 2002  PS (M.A. Thesis, San Francisco State University)

Unpublished Notes

  1. The Markov basis of K_3,N (with Johannes Rauh) 1406.5936
  2. Tight closure of monomial ideals in Fermat rings.  For Math 274, Fall 2002  PS

Research has been supported in part by the U.S. National Science Foundation and the David and Lucille Packard Foundation.