## Related Seminars

See upcoming events in our Discrete Applied Mathematics and Nonlinear Algebra and Statistics seminars.

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## Ph.D. Students

- Adam Rumpf
- William Schwartz

## Recent Research Grants

- NSF DMS-1522662 (PIs S. Petrovic and D. Stasi): Randomized Algorithms in Computational Algebra, 2015-2019.

## Recent Publications

- H. Kaul and C. Mitillos.
*On Graph Fall-Coloring: Existence and Constructions*. Submitted, 2016.
- J. A. De Loera, S. Petrovic, L. Silverstein, D. Stasi, and D. Wilburne.
*Random Monomial* Ideals.* *Journal of Algebra (2019), Vol. 519, No. 1, pp. 440-473.
- S. Petrovic.
*What is ... a Markov Basis*? Notices of the American Mathematical Society (August, 2019).
- S. Petrovic, A. Thoma, and M. Vladoiu.
* Hypergraph Encodings of Arbitrary Toric Ideals, *Journal of Combinatorial Theory, Series A (2019), Vol. 166, pp. 11-41.
- S. Petrović, A. Thoma, and M. Vladoiu.
*Bouquet Algebra of Toric Ideals*. Journal of Algebra (2018), Vol. 512, pp. 493-525.
- A. Bonato, X. Pérez-Giménez, P. Prałat, and B. Reiniger.
*The Game of Overprescribed Cops and Robbers Played on Graphs*. Graphs and Combinatorics (2017), Vol. 33, Issue 4, pp. 801-815.
- J. Carraher, W. Kinnersley, B. Reiniger, and D. B. West.
*The Game Saturation Number of a Graph*. Journal of Graph Theory (2017), Vol. 85, Issue 2, pp. 481-495.
- A. Corso, U. Nagel, S. Petrovic, and C. Yuen.
*Blow-up Algebras, Determinantal Ideals, and Dedekind-Mertens-Like Formulas*. Forum Mathematicum (2017), Vol. 29, Issue 4, pp. 799-830.
- M. Dewar, J. Healy, X. Pérez-Giménez, P. Prałat, J. Proos, B. Reiniger, and K. Ternovsky.
*Subgraphs in Non-Uniform Random Hypergraphs*. Algorithms and Models for the Web Graph, 13th International Workshop, WAW 2016, Montreal, QC, Canada, December 14-15, 2016, Proceedings (A. Bonato, F. C. Graham, and P. Prałat, eds.), Lecture Notes in Computer Science, Vol. 10088, pp. 140-151, Springer, 2017.
- M. Ferrara, B. Kay, L. Kramer, R. R. Martin, B. Reiniger, H. C. Smith, and E. Sullivan.
*The Saturation Number of Induced Subposets of the Boolean Lattice*. Discrete Mathematics (2017), Vol. 340, Issue 10, pp. 2479-2487.
- R. Fulek, M. J. Pelsmajer, and M. Schaefer.
*Hanani-Tutte for Radial Planarity.* Journal of Graph Algorithms and Applications (2017), Vol. 21, No. 1, pp. 135-154.
- E. Gross, S. Petrovic, and D. Stasi.
*Goodness of Fit for Log-Linear Network Models: Dynamic Markov Bases Using Hypergraphs.* Annals of the Institute of Statistical Mathematics (2017), Vol. 69, Issue 3, pp. 673-704.
- V. Karwa, M. J. Pelsmajer, S. Petrovic, D. Stasi, and D. Wilburne.
* Statistical Models for Cores Decomposition of an Undirected Random Graph*. Electronic Journal of Statistics (2017), Vol. 11, No. 1, pp. 1949-1982.
- S. Petrovic.
*A Survey of Discrete Methods in (Algebraic) Statistics for Networks*. Algebraic and Geometric Methods in Discrete Mathematics (H. A. Harrington, M. Omar, and M. Wright, eds.), Contemporary Mathematics, Vol. 685, pp. 260-281, American Mathematical Society, 2017.
- R. H. Sloan, D. Stasi and G. Túran.
*Hydras: Directed Hypergraphs and Horn Formulas*. Theoretical Computer Science (2017), Vol. 658, Part B, pp. 417-428.
- N. Alon, A. V. Kostochka, B. Reiniger, D. B. West, and X. Zhu.
*Coloring, Sparseness, and Girth*. Israel Journal of Mathematics (2016), Vol. 214, Issue 1, pp. 315-331.
- J. A. De Loera, S. Petrovic, and D. Stasi.
*Random Sampling in Computational Algebra: Helly Numbers and Violator Spaces.* Journal of Symbolic Computation (2016), Vol. 77, pp.1-15.
- R. Fulek, M. J. Pelsmajer, and M. Schaefer.
*Hanani-Tutte for Radial Planarity II*. Graph Drawing and Network Visualization, 24th International Symposium, GD 2016, Athens, Greece, September 19-21, 2016, Revised Selected Papers (Y. Hu and M. Nöllenburg, eds.), Lecture Notes in Computer Science, Vol. 9801, pp. 468-481, Springer, 2016.
- B. Reiniger and E. Yeager.
*Large Subposets with Small Dimension*. Order (2016), Vol. 33, Issue 1, pp. 81-84.
- S. Antaris, D. Stasi, M. Högqvist, G. Pallis, and M. D. Dikaiakos.
*A Socio-Aware Decentralized Topology Construction Protocol*. HOTWEB'15, Proceedings of the 2015 Third IEEE Workshop on Hot Topics in Web Systems and Technologies (Hotweb), pp. 91-96, Institute of Electrical and Electronics Engineers, 2015.
- J. A. De Loera, S. Marguiles, M. Pernpeintner, E. Reidl, D. Rolnic, G. Spencer, D. Stasi, and J. Swenson.
*Graph-Coloring Ideals: Nullstellensatz Certificates, Gröbner Bases for Chordal Graphs, and Hardness of Gröbner Bases*. ISSAC’15, Proceedings of the 2015 ACM, International Symposium on Symbolic and Algebraic Computation, July 6-9, 2015, Bath, UK, pp. 133-140, The Association for Computing Machinery, Inc., 2015.
- R. Fulek, M. J. Pelsmajer, and M. Schaefer.
*Hanani-Tutte for Radial Planarity*. Graph Drawing and Network Visualization, 23rd International Symposium, GD 2015, Los Angeles, CA, USA, September 24-26, 2015, Revised Selected Papers (E. D. Giacomo and A. Lubiw, eds.), Lecture Notes in Computer Science, Vol. 9411, pp. 99-110, Springer, 2015.
- A. V. Kostochka and B. Reiniger.
*The Minimum Number of Edges in a 4-Critical Graph that is Bipartite Plus 3 Edges*. European Journal of Combinatorics (2015), Vol. 46, pp. 89-94.
- A. Kündgen, M. J. Pelsmajer, and R. Ramamurthi.
*Finding Minors in Graphs with a Given Path Structure*. Journal of Graph Theory (2015), Vol. 79, Issue 1, pp. 30-47.