Seth Sullivant

Bortner, C., Gross, E., Meshkat, N., Shiu, A., & Sullivant, S. (2023). Identifiability of linear compartmental tree models and a general formula for input-output equations. ADVANCES IN APPLIED MATHEMATICS, 146. https://doi.org/10.1016/j.aam.2023.102490

Stanley, C., & Sullivant, S. (2023). On mixing behavior of a family of random walks determined by a linear recurrence. DISCRETE MATHEMATICS, 346(1). https://doi.org/10.1016/j.disc.2022.113166

Coons, J. I., & Sullivant, S. (2023). The h*-polynomial of the order polytope of the zig-zag poset. ELECTRONIC JOURNAL OF COMBINATORICS, 30(2). https://doi.org/10.37236/11526

Misra, P., & Sullivant, S. (2022). Directed Gaussian graphical models with toric vanishing ideals. ADVANCES IN APPLIED MATHEMATICS, 138. https://doi.org/10.1016/j.aam.2022.102345

Hollering, B., & Sullivant, S. (2022, January 14). Exchangeable and sampling-consistent distributions on rooted binary trees. JOURNAL OF APPLIED PROBABILITY. https://doi.org/10.1017/jpr.2021.28

Bortner, C., & Sullivant, S. (2022). Structural identifiability of series-parallel LCR systems. JOURNAL OF SYMBOLIC COMPUTATION, 112, 79–104. https://doi.org/10.1016/j.jsc.2022.01.002

Hollering, B., & Sullivant, S. (2021). Identifiability in phylogenetics using algebraic matroids. JOURNAL OF SYMBOLIC COMPUTATION, 104, 142–158. https://doi.org/10.1016/j.jsc.2020.04.012

Coons, J. I., & Sullivant, S. (2021). Quasi-independence models with rational maximum likelihood estimator. JOURNAL OF SYMBOLIC COMPUTATION, 104, 917–941. https://doi.org/10.1016/j.jsc.2020.10.006

Misra, P., & Sullivant, S. (2019). BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE FOR A GIVEN TREE SHAPE. SIAM JOURNAL ON DISCRETE MATHEMATICS, 33(4), 2316–2325. https://doi.org/10.1137/18M1213695

Sullivant, S. (2019). Strongly Robust Toric Ideals in Codimension 2. Journal of Algebraic Statistics, 10(1), 128–136. https://doi.org/10.18409/jas.v10i1.62

Sullivant, S. (2018). Algebraic Statistics. https://doi.org/10.1090/gsm/194

Durden, C., & Sullivant, S. (2018). Identifiability of Phylogenetic Parameters from k-mer Data Under the Coalescent. Bulletin of Mathematical Biology, 81(2), 431–451. https://doi.org/10.1007/s11538-018-0399-1

Gross, E., & Sullivant, S. (2018). The maximum likelihood threshold of a graph. BERNOULLI, 24(1), 386–407. https://doi.org/10.3150/16-bej881

Bernstein, D. I., & Sullivant, S. (2017). Normal Binary Hierarchical Models. EXPERIMENTAL MATHEMATICS, 26(2), 153–164. https://doi.org/10.1080/10586458.2016.1142911

Allman, E. S., Rhodes, J. A., & Sullivant, S. (2017). Statistically Consistent k-mer Methods for Phylogenetic Tree Reconstruction. JOURNAL OF COMPUTATIONAL BIOLOGY, 24(2), 153–171. https://doi.org/10.1089/cmb.2015.0216

Bernstein, D. I., & Sullivant, S. (2017). Unimodular binary hierarchical models. JOURNAL OF COMBINATORIAL THEORY SERIES B, 123, 97–125. https://doi.org/10.1016/j.jctb.2016.11.003

Rauh, J., & Sullivant, S. (2016). Lifting Markov bases and higher codimension toric fiber products. Journal of Symbolic Computation, 74, 276–307. https://doi.org/10.1016/j.jsc.2015.07.003

Fink, A., Rajchgot, J., & Sullivant, S. (2016). Matrix Schubert varieties and Gaussian conditional independence models. JOURNAL OF ALGEBRAIC COMBINATORICS, 44(4), 1009–1046. https://doi.org/10.1007/s10801-016-0698-2

Bernstein, D. I., Ho, L. S. T., Long, C., Steel, M., St John, K., & Sullivant, S. (2015). BOUNDS ON THE EXPECTED SIZE OF THE MAXIMUM AGREEMENT SUBTREE. SIAM JOURNAL ON DISCRETE MATHEMATICS, 29(4), 2065–2074. https://doi.org/10.1137/140997750

Meshkat, N., Sullivant, S., & Eisenberg, M. (2015). Identifiability Results for Several Classes of Linear Compartment Models. BULLETIN OF MATHEMATICAL BIOLOGY, 77(8), 1620–1651. https://doi.org/10.1007/s11538-015-0098-0

Long, C., & Sullivant, S. (2015). Identifiability of 3-class Jukes-Cantor mixtures. ADVANCES IN APPLIED MATHEMATICS, 64, 89–110. https://doi.org/10.1016/j.aam.2014.12.003

Long, C., & Sullivant, S. (2015). Tying up loose strands: Defining equations of the strand symmetric model. Journal of Algebraic Statistics, 6(1), 17–23. https://doi.org/10.18409/jas.v6i1.34

Davidson, R., & Sullivant, S. (2014). Distance-Based Phylogenetic Methods Around a Polytomy. IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 11(2), 325–335. https://doi.org/10.1109/tcbb.2014.2309592

Meshkat, N., & Sullivant, S. (2014). Identifiable reparametrizations of linear compartment models. JOURNAL OF SYMBOLIC COMPUTATION, 63, 46–67. https://doi.org/10.1016/j.jsc.2013.11.002

Engstrom, A., Kahle, T., & Sullivant, S. (2014). Multigraded commutative algebra of graph decompositions. JOURNAL OF ALGEBRAIC COMBINATORICS, 39(2), 335–372. https://doi.org/10.1007/s10801-013-0450-0

Kahle, T., Rauh, J., & Sullivant, S. (2014). POSITIVE MARGINS AND PRIMARY DECOMPOSITION. JOURNAL OF COMMUTATIVE ALGEBRA, 6(2), 173–208. https://doi.org/10.1216/jca-2014-6-2-173

Mahdi, A., Meshkat, N., & Sullivant, S. (2014). Structural Identifiability of Viscoelastic Mechanical Systems. PLOS ONE, 9(2). https://doi.org/10.1371/journal.pone.0086411

García-Puente, L., Petrović, S., & Sullivant, S. (2013). Graphical models. Journal of Software for Algebra and Geometry, 5(1), 1–7. https://doi.org/10.2140/jsag.2013.5.1

Davidson, R., & Sullivant, S. (2013). Polyhedral combinatorics of UPGMA cones. ADVANCES IN APPLIED MATHEMATICS, 50(2), 327–338. https://doi.org/10.1016/j.aam.2012.10.002

Draisma, J., Sullivant, S., & Talaska, K. (2013). Positivity for Gaussian graphical models. ADVANCES IN APPLIED MATHEMATICS, 50(5), 661–674. https://doi.org/10.1016/j.aam.2013.03.001

Hillar, C. J., & Sullivant, S. (2012). Finite Gröbner bases in infinite dimensional polynomial rings and applications. Advances in Mathematics, 229(1), 1–25. https://doi.org/10.1016/j.aim.2011.08.009

Ardila, F., Owen, M., & Sullivant, S. (2012). Geodesics in CAT(0) cubical complexes. ADVANCES IN APPLIED MATHEMATICS, 48(1), 142–163. https://doi.org/10.1016/j.aam.2011.06.004

Rhodes, J. A., & Sullivant, S. (2012). Identifiability of Large Phylogenetic Mixture Models. BULLETIN OF MATHEMATICAL BIOLOGY, 74(1), 212–231. https://doi.org/10.1007/s11538-011-9672-2

Sullivant, S. (2012). THE DISENTANGLING NUMBER FOR PHYLOGENETIC MIXTURES. SIAM JOURNAL ON DISCRETE MATHEMATICS, 26(2), 856–859. https://doi.org/10.1137/110843459

Allman, E. S., Rhodes, J. A., & Sullivant, S. (2012). When Do Phylogenetic Mixture Models Mimic Other Phylogenetic Models? SYSTEMATIC BIOLOGY, 61(6), 1049–1059. https://doi.org/10.1093/sysbio/sys064

Bidkhori, H., & Sullivant, S. (2011). Eulerian-Catalan numbers. Electronic Journal of Combinatorics, 18(1).

Drton, M., Foygel, R., & Sullivant, S. (2011). GLOBAL IDENTIFIABILITY OF LINEAR STRUCTURAL EQUATION MODELS. ANNALS OF STATISTICS, 39(2), 865–886. https://doi.org/10.1214/10-aos859

Allman, E. S., Petrovic, S., Rhodes, J. A., & Sullivant, S. (2011). Identifiability of Two-Tree Mixtures for Group-Based Models. IEEE-ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS, 8(3), 710–722. https://doi.org/10.1109/tcbb.2010.79

Sullivant, S. (2010). Normal binary graph models. ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS, 62(4), 717–726. https://doi.org/10.1007/s10463-010-0296-3

Sullivant, S. (2010). Normal binary graph models. Annals of the Institute of Statistical Mathematics, Special Issue: Algebraic Methods in Computational Statistics, 64(4), 717–726.

Sullivant, S., Talaska, K., & Draisma, J. (2010). TREK SEPARATION FOR GAUSSIAN GRAPHICAL MODELS. ANNALS OF STATISTICS, 38(3), 1665–1685. https://doi.org/10.1214/09-aos760

Sullivant, S. (2009). A Gröbner basis for the secant ideal of the second hypersimplex. Journal of Commutative Algebra, 1(2), 327–338. https://doi.org/10.1216/jca-2009-1-2-327

Putinar, M., & Sullivant, S. (Eds.). (2009). Emerging Applications of Algebraic Geometry. In The IMA Volumes in Mathematics and its Applications. https://doi.org/10.1007/978-0-387-09686-5

Sullivant, S. (2009, August). Gaussian conditional independence relations have no finite complete characterization. JOURNAL OF PURE AND APPLIED ALGEBRA, Vol. 213, pp. 1502–1506. https://doi.org/10.1016/j.jpaa.2008.11.026

Drton, M., Sturmfels, B., & Sullivant, S. (2009). Lectures on Algebraic Statistics. https://doi.org/10.1007/978-3-7643-8905-5

Beerenwinkel, N., & Sullivant, S. (2009). Markov models for accumulating mutations. BIOMETRIKA, 96(3), 645–661. https://doi.org/10.1093/biomet/asp023

Sidman, J., & Sullivant, S. (2009). Prolongations and Computational Algebra. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 61(4), 930–949. https://doi.org/10.4153/CJM-2009-047-5

Sullivant, S. (2008). Algebraic geometry of Gaussian Bayesian networks. Advances in Applied Mathematics, 40(4), 482–513. https://doi.org/10.1016/j.aam.2007.04.004

Sullivant, S. (2008). Combinatorial symbolic powers. Journal of Algebra, 319(1), 115–142. https://doi.org/10.1016/j.jalgebra.2007.09.024

Sturmfels, B., & Sullivant, S. (2008). Toric geometry of cuts and splits. The Michigan Mathematical Journal, 57(0), 689–709. https://doi.org/10.1307/mmj/1220879432

Hoşten, S., & Sullivant, S. (2007). A finiteness theorem for Markov bases of hierarchical models. Journal of Combinatorial Theory, Series A, 114(2), 311–321. https://doi.org/10.1016/j.jcta.2006.06.001

Drton, M., & Sullivant, S. (2007). Algebraic statistical models. Statistica Sinica, 17(4), 1273–1297.

Sullivant, S. (2007). Toric fiber products. Journal of Algebra, 316(2), 560–577. https://doi.org/10.1016/j.jalgebra.2006.10.004

Drton, M., Sturmfels, B., & Sullivant, S. (2006). Algebraic factor analysis: tetrads, pentads and beyond. Probability Theory and Related Fields, 138(3-4), 463–493. https://doi.org/10.1007/s00440-006-0033-2

Sturmfels, B., & Sullivant, S. (2006). Combinatorial secant varieties. Quarterly Journal of Pure and Applied Mathematics, 2, 285–309.

Sullivant, S. (2006). Compressed polytopes and statistical disclosure limitation. Tohoku Mathematical Journal, 58(3), 433–445. https://doi.org/10.2748/tmj/1163775139

Eriksson, N., Fienberg, S. E., Rinaldo, A., & Sullivant, S. (2006). Polyhedral conditions for the nonexistence of the MLE for hierarchical log-linear models. Journal of Symbolic Computation, 41(2), 222–233. https://doi.org/10.1016/j.jsc.2005.04.003

Chen, Y., Dinwoodie, I. H., & Sullivant, S. (2006). Sequential importance sampling for multiway tables. The Annals of Statistics, 34(1), 523–545. https://doi.org/10.1214/009053605000000822

Slavkovic, A. B., & Sullivant, S. (2006). The space of compatible full conditionals is a unimodular toric variety. Journal of Symbolic Computation, 41(2), 196–209. https://doi.org/10.1016/j.jsc.2005.04.006

Sullivant, S. (2005). Small Contingency Tables with Large Gaps. SIAM Journal on Discrete Mathematics, 18(4), 787–793. https://doi.org/10.1137/s0895480104444090

Sturmfels, B., & Sullivant, S. (2005). Toric Ideals of Phylogenetic Invariants. Journal of Computational Biology, 12(2), 204–228. https://doi.org/10.1089/cmb.2005.12.204

Dobra, A., & Sullivant, S. (2004). A Divide-and-Conquer Algorithm for Generating Markov Bases of Multi-way Tables. Computational Statistics, 19(3), 347–366. https://doi.org/10.1007/bf03372101

Hoşten, S., & Sullivant, S. (2004). Ideals of adjacent minors. Journal of Algebra, 277(2), 615–642. https://doi.org/10.1016/j.jalgebra.2004.01.027

Sullivant, S., & Develin, M. (2003). Markov Bases of Binary Graph Models. Annals of Combinatorics, 7(4), 441–466. https://doi.org/10.1007/s00026-003-0196-9

Hoşten, S., & Sullivant, S. (2002). Gröbner Bases and Polyhedral Geometry of Reducible and Cyclic Models. Journal of Combinatorial Theory, Series A, 100(2), 277–301. https://doi.org/10.1006/jcta.2002.3301