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
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
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
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
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
Structural identifiability of series-parallel LCR systems
Cashous Bortner, Seth Sullivant Journal of Symbolic Computation,112 (2022) 79-104 2107.06271
Gaussian graphical models with toric vanishing ideals
Pratik Misra, Seth Sullivant Annals of the Institute of Statistical Mathematics73 (2021) no.4,757-785. 1912.02265
Quasi-independence models with rational maximum likelihood estimates
Jane Ivy Coons, Seth Sullivant Journal of Symbolic Computation, 104 (2021), 917–941. 2006.06832
Identifiability in phylogenetics using algebraic matroids
Benjamin Hollering, Seth Sullivant Journal of Symbolic Computation 104 (2021),142–158. 1909.13754
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
Bounds on the expected size of the maximum agreement subtree for a given tree shape
Pratik Misra, Seth Sullivant SIAM Journal on Discrete Mathematics33 (2019) no. 4, 2316-2325 1809.04488
Strongly robust toric ideals in codimension 2
Seth Sullivant Journal of Algebraic Statistics10 (2019) no.1, 128-136. 1610.07476
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
The maximum likelihood threshold of a graph
Elizabeth Gross, Seth Sullivant Bernoulli 24 (2018), no. 1, 386–407. 1404.6989
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. 1511.01956Supplementary Materials
Unimodular binary hierarchical models
Daniel I. Bernstein, Seth Sullivant Journal of Combinatorial Theory: Series B 123 (2017), 97–125. 1502.06131Supplementary Materials
Normal binary hierarchical models
Daniel I. Bernstein, Seth Sullivant Experimental Mathematics 26 (2017), no. 2, 153–164. 1508.05461
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
Lifting Markov bases and higher codimension toric fiber products
Johannes Rauh, Seth Sullivant J. Symbolic Comput. 74 (2016), 276–307. 1404.6392
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
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
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. 1410.3344Supplementary Materials
Identifiability of Jukes-Cantor 3-tree mixtures
Colby Long, Seth Sullivant Adv. in Appl. Math.64 (2015), 89–110. 1406.7256Supplementary Materials
Distance-based phylogenetic algorithms around a polytomy
Ruth Davidson, Seth Sullivant IEEE/ACM Transactions in Computational Biology and Bioinformatics 11 (2014) 325-335 1307.5908Supplementary Materials
Positive margins and primary decomposition.
Thomas Kahle, Johannes Rauh, Seth Sullivant Journal of Commutative Algebra6 (2), (2014), pp 173-208. 1201.2591
Structural identifiability of viscoelastic mechanical systems
Adam Mahdi, Nicolette Meshkat, Seth Sullivant PLOS One 9 (2014): e864111 1308.4950
Identifiable reparametrizations of linear compartment models
Nicolette Meshkat, Seth Sullivant Journal of Symbolic Computation 63 (2014), 46–67. 1305.5768
Multigraded commutative algebra of graph decompositions.
Alexander Engström, Thomas Kahle, Seth Sullivant J. Algebraic Combinatorics 39 (2014) no. 2, 335-372 1102.2601
Graphical models in Macaulay2
Luis Garcia-Puente, Sonja Petrovic, Seth Sullivant Journal of Software for Algebra and Geometry 5 (2013) 1208.6550 Code
Positivity for Gaussian graphical models
Jan Draisma, Seth Sullivant, Kelli Talaska Adv. in Appl. Math. 50 (2013), no. 5, 661–674. 1210.0390
Polyhedral combinatorics of UPGMA cones
Ruth Davidson, Seth Sullivant Adv. in Appl. Math.50 (2013), no. 2, 327–338. 1206.1621 Supplementary Materials
When do phylogenetic mixture models mimic other phylogenetic models?
Elizabeth Allman, John Rhodes, Seth Sullivant Systematic Biology (2012) 61 (6): 1049-1059 1202.2396
The disentangling number for phylogenetic mixtures.
Seth Sullivant SIAM Journal on Discrete Mathematics26-2 (2012), pp. 856-859
1107.2880
Identifiability of large phylogenetic mixture models.
John Rhodes, Seth Sullivant Bull. Math. Biol.74 (2012), no. 1, 212–231. 1011.4134
Finite Gröbner bases in infinite dimensional polynomial rings and applications.
Christopher Hillar, Seth Sullivant Advances in Mathematics221 (2012) 1-25 0908.1777
Geodesics in CAT(0) cubical complexes.
Federico Ardila, Megan Owen, Seth Sullivant Advances in Applied Mathematics48 (2012) 142-163 1101.2428
Global identifiability of linear structural equation models
Mathias Drton, Rina Foygel, Seth Sullivant Annals of Statistics 39 (2011):865-886. 1003.1146
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. 0909.1854Supplementary Materials
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
Trek separation for Gaussian graphical models.
Kelli Talaska, Seth Sullivant, Jan Draisma Annals of Statistics 38 no.3 (2010) 1665-1685 0812.1938
Markov models for accumulating mutations.
Niko Beerenwinkel, Seth Sullivant Biometrika96 no. 3 (2009) 645-661 0709.2646
Prolongations and computational algebra.
Jessica Sidman, Seth Sullivant Canadian Journal of Mathematics61 no. 4 (2009) 930-949 math.AC/0611696
A Gröbner basis for the secant ideal of the second hypersimplex.
Seth Sullivant Journal of Commutative Algebra 1 no.2 (2009) 0804.2897
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
Toric geometry of cuts and splits.
Bernd Sturmfels, Seth Sullivant Michigan Mathematical Journal57 (2008) 689-709 (special issue in honor of Mel Hochster) math.AC/0606683
Algebraic geometry of Gaussian Bayesian networks.
Seth Sullivant Adv. in Appl. Math.40 (2008), no. 4, 482--513. 0704.0918
Algebraic factor analysis: tetrads, pentads, and beyond.
Mathias Drton, Bernd Sturmfels, Seth Sullivant Probability Theory and Related Fields138 (2007), no. 3-4, 463--493. math.ST/0509390
A finiteness theorem for Markov bases of hierarchical models.
Serkan Hosten, Seth Sullivant J. Combin. Theory Ser. A114 (2007), no. 2, 311--321. math.CO/0401379
Combinatorial secant varieties.
Bernd Sturmfels, Seth Sullivant Quarterly Journal of Pure and Applied Mathematics2 (2006) 285-309 (Special issue in honor of Robert Macpherson) math.AC/0506223
Compressed polytopes and statistical disclosure limitation.
Seth Sullivant Tohoku Math. J. (2) 58 (2006), no. 3, 433--445. math.CO/0412535
Sequential importance sampling for multiway tables.
Yuguo Chen Ian Dinwoodie, Seth Sullivant Annals of Statistics (2006) 34 No. 1, 523-545 math.ST/0605615
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
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
Small contingency tables with large gaps.
Seth Sullivant SIAM Journal of Discrete Mathematics 18 (2005) no.4, 787-793 math.OC/0405038
Toric ideals of phylogenetic invariants
Bernd Sturmfels, Seth Sullivant Journal of Computational Biology12 (2005) 204-228. q-bio.PE/0402015
Ideals of adjacent minors
Serkan Hosten, Seth Sullivant Journal of Algebra277 (2004), 615-642 math.AC/0306318
A divide-and-conquer algorithm for generating Markov bases of multi-way tables
Adrian Dobra, Seth Sullivant Computational Statistics19 (2004), 347-366
Markov bases of binary graph models
Mike Develin, Seth Sullivant Annals of Combinatorics 7 (2003), 441-466 math.CO/0308280
Gröbner bases and polyhedral geometry of reducible and cyclic models
Serkan Hosten, Seth Sullivant Journal of Combinatorial Theory: Series A100 (2002) no. 2, 277-301
Conference Proceedings and Book Chapters
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
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
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
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
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.
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
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.
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
Toric ideals in algebraic statistics, 2005 pdf.
(Ph. D. Thesis, UC Berkeley)
Algebraic geometry and combinatorics of hierarchical models, 2002PS
(M.A. Thesis, San Francisco State University)
Unpublished Notes
Sequential importance sampling for the Ising model
Jing Xi, Seth Sullivant 1410.4217
The Markov basis of K_3,N
Johannes Rauh, Seth Sullivant 1406.5936
Tight closure of monomial ideals in Fermat rings
Seth Sullivant
For Math 274, Fall 2002 PS
