Publications

Books

  1. Algebraic Statistics
    Seth Sullivant
    American Mathematical Society, Graduate Studies in Mathematics, 194, 2018, 490pp.
  2. Lectures on Algebraic Statistics
    Mathias Drton, Bernd Sturmfels, Seth Sullivant
    Oberwolfach Seminar Series 39, Birkhauser, 2009
  3. Emerging Applications of Algebraic Geometry
    Mihai Putinar, Seth Sullivant (editors),
    IMA Series 149, Springer, 2008

Preprints

  1. The h*-polynomial of the order polytope of the zig-zag poset
    Jane Ivy Coons, Seth Sullivant
    To appear in Electronic Journal of Combinatorics
    1901.07443

Journal papers

  1. On mixing behavior of a family of random walks determined by a linear recurrence
    Caprice Stanley, Seth Sullivant
    Discrete Math. 346 (2023), no. 1, Paper No. 113166, 11 pp.
    1710.03845 
  2. Identifiability of linear compartmental tree models
    Cashous Bortner, Elizabeth Gross, Nicolette Meshkat, Anne Shiu, Seth Sullivant
    Adv. in Appl. Math. 146 (2023),Paper No. 102490, 38 pp.
    2106.08487
  3. Directed Gaussian graphical models with toric vanishing ideals
    Pratik Misra, Seth Sullivant
    Advances in Applied Math. 138 (2022)  Paper No. 102345, 38 pp.
    2105.13357
  4. Exchangeable and sampling consistent distributions on rooted binary trees
    Benjamin Hollering, Seth Sullivant
    Journal of Applied Probability 59 (2022) no. 1, 60-80.
    1902.03321
  5. Structural identifiability of series-parallel LCR systems
    Cashous Bortner, Seth Sullivant
    Journal of Symbolic Computation, 112 (2022) 79-104
    2107.06271
  6. Discrete max-linear Bayesian networks
    Benjamin Hollering, Seth Sullivant
    Algebraic Statistics  12 (2021), no. 2, 213–225.
    2102.03426
  7. Gaussian graphical models with toric vanishing ideals
    Pratik Misra, Seth Sullivant
    Annals of the Institute of Statistical Mathematics 73 (2021) no.4,757-785.
    1912.02265
  8. Quasi-independence models with rational maximum likelihood estimates
    Jane Ivy Coons, Seth Sullivant
    Journal of Symbolic Computation, 104 (2021), 917–941.
    2006.06832
  9. Identifiability in phylogenetics using algebraic matroids
    Benjamin Hollering, Seth Sullivant
    Journal of Symbolic Computation 104 (2021),142–158.
    1909.13754
  10. Toric geometry of the Cavender-Farris-Neyman model with a molecular clock
    Jane Ivy Coons, Seth Sullivant
    Advances  in Applied Mathematics. 123 (2021), 102119, 54 pp.
    1805.04175 
  11. Bounds on the expected size of the maximum agreement subtree for a given tree shape
    Pratik Misra, Seth Sullivant
    SIAM Journal on Discrete Mathematics 33 (2019) no. 4, 2316-2325
    1809.04488
  12. Strongly robust toric ideals in codimension 2
    Seth Sullivant
    Journal of Algebraic Statistics 10 (2019) no.1, 128-136.
    1610.07476 
  13. Identifiability of phylogenetic parameters from k-mer data under the coalescent
    Chris Durden, Seth Sullivant
    Bulletin of Mathematical Biology Special Issue on Algebraic Methods in Phylogenetics (2018) 1-21.
    1705.06993
  14. The maximum likelihood threshold of a graph
    Elizabeth Gross, Seth Sullivant
    Bernoulli 24 (2018), no. 1, 386–407.
    1404.6989 
  15. Statistically consistent k-mer methods for phylogenetic tree reconstruction
    Elizabeth Allman, John Rhodes, Seth Sullivant
    Journal of Computational Biology February 2017, 24(2): 153-171.
    1511.01956 Supplementary Materials
  16. Unimodular binary hierarchical models
    Daniel I. Bernstein, Seth Sullivant
    Journal of Combinatorial Theory: Series B 123 (2017), 97–125.
    1502.06131 Supplementary Materials 
  17. Normal binary hierarchical models
    Daniel I. Bernstein, Seth Sullivant
    Experimental Mathematics 26 (2017), no. 2, 153–164.
    1508.05461
  18. Matrix Schubert varieties and Gaussian conditional independence models
    Alex Fink, Jenna Rajchgot, Seth Sullivant
    Journal of Algebraic Combinatorics, 44 (2016), no. 4, 1009-1046.
    1510.04124
  19. Lifting Markov bases and higher codimension toric fiber products
    Johannes Rauh, Seth Sullivant
    J. Symbolic Comput. 74 (2016), 276–307.
    1404.6392
  20. Identifiability results for several classes of linear compartment models
    Nicolette Meshkat, Marisa Eisenberg, Seth Sullivant
    Bull. Math. Biol. 77 (2015), no. 8, 1620–1651.
    1410.8587
  21. Bounds on the expected size of the maximum agreement subtree
    Daniel I. Bernstein, Lam Ho, Colby Long, Mike Steel, Katherine St. John, Seth Sullivant
    SIAM J. Discrete Math. 29 (2015), no. 4, 2065–2074.
    1411.7338
  22. Tying up loose strands: the defining equations of the strand symmetric model
    Colby Long, Seth Sullivant
    J. Algebr. Stat. 6 (2015), no. 1, 17–23.
    1410.3344   Supplementary Materials 
  23. Identifiability of Jukes-Cantor 3-tree mixtures
    Colby Long, Seth Sullivant
    Adv. in Appl. Math. 64 (2015), 89–110.
    1406.7256 Supplementary Materials 
  24. Distance-based phylogenetic algorithms around a polytomy
    Ruth Davidson, Seth Sullivant
    IEEE/ACM Transactions in Computational Biology and Bioinformatics 11 (2014) 325-335
    1307.5908   Supplementary Materials
  25. Positive margins and primary decomposition.
    Thomas Kahle, Johannes Rauh, Seth Sullivant
    Journal of Commutative Algebra 6 (2), (2014), pp 173-208.
    1201.2591
  26. Structural identifiability of viscoelastic mechanical systems
    Adam Mahdi, Nicolette Meshkat, Seth Sullivant
    PLOS One 9 (2014): e864111
    1308.4950
  27. Identifiable reparametrizations of linear compartment models
    Nicolette Meshkat, Seth Sullivant
    Journal of Symbolic Computation 63 (2014), 46–67.
    1305.5768
  28. Multigraded commutative algebra of graph decompositions.
    Alexander Engström, Thomas Kahle, Seth Sullivant
    J. Algebraic Combinatorics 39 (2014) no. 2, 335-372
    1102.2601
  29. Graphical models in Macaulay2
    Luis Garcia-Puente, Sonja Petrovic, Seth Sullivant
    Journal of Software for Algebra and Geometry 5 (2013)
    1208.6550 Code
  30. Positivity for Gaussian graphical models
    Jan Draisma, Seth Sullivant, Kelli Talaska
    Adv. in Appl. Math. 50 (2013), no. 5, 661–674.
    1210.0390
  31. Polyhedral combinatorics of UPGMA cones
    Ruth Davidson, Seth Sullivant
    Adv. in Appl. Math. 50 (2013), no. 2, 327–338.
    1206.1621   Supplementary Materials 
  32. When do phylogenetic mixture models mimic other phylogenetic models?
    Elizabeth Allman, John Rhodes, Seth Sullivant
    Systematic Biology (2012) 61 (6): 1049-1059
    1202.2396
  33. The disentangling number for phylogenetic mixtures.
    Seth Sullivant
    SIAM Journal on Discrete Mathematics 26-2 (2012), pp. 856-859
    1107.2880 
  34. Identifiability of large phylogenetic mixture models.
    John Rhodes, Seth Sullivant
    Bull. Math. Biol. 74 (2012), no. 1, 212–231.
    1011.4134 
  35. Finite Gröbner bases in infinite dimensional polynomial rings and applications.
    Christopher Hillar, Seth Sullivant
    Advances in Mathematics 221 (2012) 1-25
    0908.1777
  36. Geodesics in CAT(0) cubical complexes.
    Federico Ardila, Megan Owen, Seth Sullivant
    Advances in Applied Mathematics 48 (2012) 142-163
    1101.2428
  37. Eulerian-Catalan numbers.
    Hoda Bidkhori, Seth Sullivant
    Electronic Journal of Combinatorics 18 no.1 (2011) #P187
    1101.1108
  38. Global identifiability of linear structural equation models
    Mathias Drton, Rina Foygel, Seth Sullivant
    Annals of Statistics 39 (2011):865-886.
    1003.1146
  39. Identifiability of two-tree mixtures for group-based models.
    Elizabeth Allman, Sonja Petrovic, John Rhodes, Seth Sullivant
    IEEE/ACM Transactions in Computational Biology and Bioinformatics, 8 no. 3 (2011) 710-722.
    0909.1854   Supplementary Materials 
  40. Normal binary graph models.
    Seth Sullivant
    Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics, 64 no.4 (2010) 717-726
    0906.1784
  41. Trek separation for Gaussian graphical models.
    Kelli Talaska, Seth Sullivant, Jan Draisma
    Annals of Statistics 38 no.3 (2010) 1665-1685
    0812.1938
  42. Markov models for accumulating mutations.
    Niko Beerenwinkel, Seth Sullivant
    Biometrika 96 no. 3 (2009) 645-661
    0709.2646 
  43. Prolongations and computational algebra.
    Jessica Sidman, Seth Sullivant
    Canadian Journal of Mathematics 61 no. 4 (2009) 930-949
    math.AC/0611696
  44. A Gröbner basis for the secant ideal of the second hypersimplex.
    Seth Sullivant
    Journal of Commutative Algebra 1 no.2 (2009)
    0804.2897
  45. Gaussian conditional independence relations have no finite complete characterization.
    Seth Sullivant
    Journal of Pure and Applied Algebra, 213 (2009) 1502-1506 (special issue on Theoretical and Practical Effectivity of Gröbner Bases)
    0704.2847
  46. Toric geometry of cuts and splits.
    Bernd Sturmfels, Seth Sullivant
    Michigan Mathematical Journal 57 (2008) 689-709 (special issue in honor of Mel Hochster)
    math.AC/0606683
  47. Algebraic geometry of Gaussian Bayesian networks.
    Seth Sullivant
    Adv. in Appl. Math. 40 (2008), no. 4, 482--513.
    0704.0918
  48. Combinatorial symbolic powers.
    Seth Sullivant
    J. Algebra 319 (2008), no. 1, 115--142.
    math.AC/0608542
  49. Algebraic statistical models.
    Mathias Drton, Seth Sullivant
    Statist. Sinica 17 (2007), no. 4, 1273--1297.
    math.ST/0703609
  50. Toric fiber products.
    Seth Sullivant
    J. Algebra 316 (2007), no. 2, 560--577.
    math.AC/0602052
  51. Algebraic factor analysis:  tetrads, pentads, and beyond.
    Mathias Drton, Bernd Sturmfels, Seth Sullivant
    Probability Theory and Related Fields  138 (2007), no. 3-4, 463--493.
    math.ST/0509390
  52. A finiteness theorem for Markov bases of hierarchical models.
    Serkan Hosten, Seth Sullivant
    J. Combin. Theory Ser. A  114  (2007),  no. 2, 311--321.
    math.CO/0401379
  53. Combinatorial secant varieties.
    Bernd Sturmfels, Seth Sullivant
    Quarterly Journal of Pure and Applied Mathematics 2 (2006) 285-309  (Special issue in honor of Robert Macpherson)
    math.AC/0506223
  54. Compressed polytopes and statistical disclosure limitation.
    Seth Sullivant
    Tohoku Math. J. (2)  58  (2006),  no. 3, 433--445.
    math.CO/0412535
  55. Sequential importance sampling for multiway tables.
    Yuguo Chen Ian Dinwoodie, Seth Sullivant
    Annals of Statistics (2006) 34 No. 1, 523-545
    math.ST/0605615
  56. Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models.
    Nicholas Eriksson, Stephen E. Fienberg, Alessandro Rinaldo, Seth Sullivant
    Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006)  222-233
    math.CO/0405044
  57. The space of compatible full conditionals is a unimodular toric variety
    Aleksandra Slavkovic, Seth Sullivant
    Journal of Symbolic Computation, Special issue on Computational Algebraic Statistics 41 (2006) 196-209
    math.AG/0405046
  58. Small contingency tables with large gaps.
    Seth Sullivant
    SIAM Journal of Discrete Mathematics  18 (2005) no.4, 787-793
    math.OC/0405038
  59. Toric ideals of phylogenetic invariants
    Bernd Sturmfels, Seth Sullivant
    Journal of Computational Biology 12 (2005) 204-228.
    q-bio.PE/0402015
  60. Ideals of adjacent minors
    Serkan Hosten, Seth Sullivant
    Journal of Algebra  277 (2004), 615-642
    math.AC/0306318
  61. A divide-and-conquer algorithm for generating Markov bases of multi-way tables
    Adrian Dobra, Seth Sullivant
    Computational Statistics  19 (2004), 347-366
  62. Markov bases of binary graph models
    Mike Develin, Seth Sullivant
    Annals of Combinatorics  7 (2003), 441-466
    math.CO/0308280
  63. Gröbner bases and polyhedral geometry of reducible and cyclic models
    Serkan Hosten, Seth Sullivant
    Journal of Combinatorial Theory: Series A 100 (2002) no. 2, 277-301

Conference Proceedings and Book Chapters

  1. Markov equivalence of max-linear Bayesian networks
    Carlos Améndola, Benjamin Hollering, Seth Sullivant, Ngoc Tran
    Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence, PMLR 161:1746-1755 (2021)
    2106.08305
  2. Algebraic aspects of conditional independence and graphical models.
    Thomas Kahle, Johannes Rauh, Seth Sullivant
    In Handbook of Graphical Models, CRC Press (Editors: Mathis Drton, Steffen Lauritzen, Marloes Matthuis, Martin Wainwright), 2018, 79-98.
    1705.07411 
  3. Algebraic tools for the analysis of state space models
    Nicolette Meshkat, Zvi Rosen, Seth Sullivant
    The 50th anniversary of Gröbner bases. Proceedings of Mathematical Society of Japan, 2015 Summer Institute, ASPM 77, 171-205
    1609.07985 
  4. Identifying causal effects with computer algebra
    Luis Garcia-Puente, Sarah Spielvogel, Seth Sullivant
    Uncertainty in Artificial Intelligence, Proceedings of the 26th Conferences, AUAI Press, 2010.
    1007.3784
  5. Algebraic complexity of maximum likelihood estimation for bivariate missing data.
    Serkan Hosten, Seth Sullivant
    Book chapter in the book Algebraic and Geometric Methods in Statistics, Cambridge University Press, 2009. ISBN-13: 9780521896191
    arXiv:0709.0935.
  6. Phylogenetic algebraic geometry
    Nicholas Eriksson, Kristian Ranestad, Bernd Sturmfels, Seth Sullivant),
    in Projective Varieties with Unexpected Properties, edited by C. Ciliberto, et al.,  Walter de Gruyter, Berlin, 2005
    math.AG/0407033
  7. Catalog of small trees.
    Marta Casanellas, Luis Garcia-Puente, Seth Sullivant
    in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.
  8. The strand symmetric model.
    Marta Casanellas, Seth Sullivant
    in Algebraic Statistics for Computational Biology, edited by L. Pachter and B. Sturmfels, Cambridge University Press, Cambridge, 2005.

Theses

  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. Sequential importance sampling for the Ising model
    Jing Xi, Seth Sullivant
    1410.4217
  2. The Markov basis of K_3,N
    Johannes Rauh, Seth Sullivant
    1406.5936
  3. Tight closure of monomial ideals in Fermat rings
    Seth Sullivant
    For Math 274, Fall 2002  PS